# install.packages("pacman")
pacman::p_load(mgcv, # For fitting Generalized Additive Models (GAMs) and Hierarchical GAMs
dplyr, # For data manipulation
ggplot2, # For data visualization
tidyr, # For reshaping and tidying data
mvtnorm, # For working with multivariate normal and t-distributions
gratia, # For visualizing and interpreting GAMs fitted with mgcv
here, # For handling file paths relative to the project root
gridExtra, # For arranging multiple ggplot2 plots into grids
mvgam, # For fitting multivariate/State-Space GAMs and plotting model components
marginaleffects, # For obtaining marginal/average predictions from fitted models
tidyverse, # For the full suite of tidy tools (read, wrangle, plot) in one load
cmdstanr) # For fitting Stan models via CmdStan, backend for mvgamLevelling up: How to unlock ecological and evolutionary data with hierarchical - Supplementary Material
1 Overview
This document provides the detailed code and supplementary materials for the article “Levelling up: How to unlock ecological data with hierarchical generalized additive models.”
It is divided as so:
Supplementary Material 1: Description of the data used throughout the study and across all coding examples (Boxes).
Supplementary Material 2: Code for Box 1 (Trends), corresponding to the section Estimating a hierarchy of trends in the article.
Supplementary Material 3: Code for Boxes 2 (Variance) and 3 (Prediction), which correspond respectively to the sections Unpacking meaningful variance and covariances from noisy biological data and Borrowing strength to boost predictions.
Most of the code presented here builds upon the examples and model structures introduced in Pedersen et al. (2019) and the various blog posts of Nicholas Clark (https://ecogambler.netlify.app/blog/).
2 Supplementary Material 1
2.1 Description of the data
We use the North American Breeding Bird Survey dataset extracted from BioTIME (Pardieck et al., 2015), a long-term monitoring program of North American bird populations that began in 1966. Our analyses focus on two subsets of the original dataset:
data_195: It is a cleaned subset of the original BioTIME data, containing only the 309 species with consistent observations between 1978 and 2007 (see Supplementary Material 2).d_crop: It is a spatially cropped subset ofdata_195, containing only observations from Waverly, New York (latitude 44.55, longitude −74.4833). To create this localized dataset, non-essential columns were removed, and records were filtered to retain only species with complete 30-year time series at this site. One species (Vireo olivaceus) was further excluded due to inconsistent data (see Supplementary Material 3).
Table S1 presents the species used in the different coding examples (Boxes), which vary from one box to another according to the objectives and requirements of each example.
Table S1. Bird species and their inclusion (indicated by tick marks) in the coding examples presented in Boxes 1, 2, and 3. Box 1 uses the broader dataset (data_195), which includes randomly selected species from the North American Breeding Bird Survey as curated in BioTIME (Pardieck et al., 2015; Dornelas et al., 2018). Boxes 2 and 3 use the spatially cropped dataset (d_crop), restricted to observations from Waverly, New York (latitude 44.55, longitude −74.4833) collected between 1978 and 2007, and feature a subset of the most common species.Altogether, 36 bird species are represented across the three boxes.
| Box | ||||
|---|---|---|---|---|
| Common name | Species name | 1 | 2 | 3 |
| Red-winged blackbird | Agelaius phoeniceus | x | x | x |
| Northern cardinal | Cardinalis cardinalis | x | ||
| Hermit thrush | Chaetura pelagica | x | x | |
| Chimney swift | Chaetura pelagica | x | ||
| Northern flicker | Colaptes auratus | x | ||
| Rock pigeon | Columba livia | x | ||
| Eastern wood-pewee | Contopus virens | x | ||
| American crow | Corvus brachyrhynchos | x | ||
| Blue jay | Cyanocitta cristata | x | ||
| Downy woodpecker | Dryobates pubescens | x | ||
| Gray catbird | Dumetella carolinensis | x | ||
| Common yellowthroat | Geothlypis trichas | x | ||
| Barn swallow | Hirundo rustica | x | ||
| Song sparrow | Melospiza melodia | x | x | x |
| Black-and-white warbler | Mniotilta varia | x | x | |
| Brown-headed cowbird | Molothrus ater | x | ||
| Great crested flycatcher | Myiarchus crinitus | x | ||
| House sparrow | Passer domesticus | x | ||
| Indigo bunting | Passerina cyanea | x | ||
| Common grackle | Quiscalus quiscula | x | ||
| Eastern phoebe | Sayornis phoebe | x | ||
| Ovenbird | Seiurus aurocapilla | x | x | |
| Yellow-rumped warbler | Setophaga coronata | x | x | |
| Black-throated green warbler | Setophaga virens | x | x | |
| American goldfinch | Spinus tristis | x | x | x |
| Chipping sparrow | Spizella passerina | x | ||
| Field sparrow | Spizella pusilla | x | ||
| Eastern meadowlark | Sturnella magna | x | ||
| Common starling | Sturnus vulgaris | x | ||
| Brown trasher | Toxostoma rufum | x | ||
| Northern house wren | Troglodytes aedon | x | ||
| American robin | Turdus migratorius | x | x | x |
| Eastern kingbird | Tyrannus tyrannus | x | ||
| Red-eyed vireo | Vireo olivaceus | x | ||
| Blue-headed vireo | Vireo solitarius | x | x | |
| Mourning dove | Zenaida macroura | x |
3 Supplementary Material 2 - Box 1
3.1 Step 1: Setting up the work environment
3.1.1 Packages and Libraries
Here, we install and load the packages required for the coding examples.
3.1.2 Import the raw data
We import the raw BBS data downloaded from BioTIME.
df <- read.csv(here::here("data", "clean", "data_195.csv"))3.1.3 Make a subset of the data (data_195)
This dataset is the subset used in the coding example presented in Box 1. It also serves as the source for the additional subset used in Boxes 2 and 3 (see Supplementary Material 3).
# Filter to years in common across many species
df_years = df |>
group_by(valid_name) |>
summarise("min_year" = min(YEAR),
"max_year" = max(YEAR))
# Look for the most common minimum and maximum years
df_years$min_year |> table()
1978
309
df_years$max_year |> table()
2007
309
# 309 species to keep
sp_to_keep = df_years |> filter(min_year == 1978, max_year == 2007)
# Cut to species that have data between 1978 and 2007
data_195 = df |> filter(valid_name %in% sp_to_keep$valid_name)3.2 Step 2: Structure the data for analysis
We process the data by selecting the 30 most abundant species for the analyses. For this Box, we use the
# Aggregating biomass data to get a yearly abundance for each species.
community_ts <- data_195 %>%
filter(!is.na(YEAR) & !is.na(valid_name) & valid_name != "") %>%
group_by(YEAR, valid_name) %>%
summarise(ABUNDANCE = n(), .groups = 'drop') %>%
rename(year = YEAR, species = valid_name, abundance = ABUNDANCE)
# Selecting the top 30 most frequently observed species (i.e., highest in abundance)
top_species <- community_ts %>% # Identify the top 30 species
group_by(species) %>%
summarise(total_abundance = sum(abundance)) %>%
arrange(desc(total_abundance)) %>%
slice_head(n = 30) %>%
pull(species)
community_ts_subset <- community_ts %>% # Create a new table with only the top 30 species
filter(species %in% top_species) %>%
mutate(species = as.factor(species))
head(community_ts_subset) # The subset of data that we will use from this point on in this section (Box 1)# A tibble: 6 × 3
year species abundance
<int> <fct> <int>
1 1978 Agelaius phoeniceus 406
2 1978 Cardinalis cardinalis 279
3 1978 Chaetura pelagica 284
4 1978 Colaptes auratus 342
5 1978 Columba livia 246
6 1978 Contopus virens 276
3.3 Step 3: Fit Model GS
Here, we fit the “GS” model described in Pedersen et al. (2019). Since the response variable represents abundance (count) data, we use the Poisson family.
# MODEL: The 'GS' Model (Global smooth + species-specific deviations)
gam_model_GS <- gam(
# Global relationship
abundance ~ s(year, bs = "tp") +
# Species-specific smoother: a factor-smoother interaction of year and species
s(year, by = species, bs = "fs") +
# Species as random effects (gives an intercept per species)
s(species, bs="re"),
# Data
data = community_ts_subset,
# Distribution family: Poisson for count data
family = poisson(),
# Estimating smoothing parameters using restricted maximum likelihood (REML)
method = "REML"
)3.4 Step 4: Derivatives and Indicators
In this section, we generate predictions and calculate community-level indicators from the fitted GS model. We first create a prediction dataset covering all species and years, and use a small value (ε) to approximate derivatives numerically. We then draw 250 posterior simulations from the model coefficients to account for parameter uncertainty. Using these simulations, we compute predicted abundances and their first derivatives, which are used to estimate per capita rates of change. Finally, we summarize these results to obtain three community indicators for each year: the mean rate of change, the mean per capita rate of change, and the standard deviation of per capita rates of change, along with their median and 95% confidence intervals.
# Create a prediction dataset
predict_data <- community_ts_subset %>%
select(year, species) %>%
distinct()
# Define a small number 'eps' for numerical differentiation
eps <- 1e-7 # Define a small number epsilon ε 'eps'
predict_data_p_eps <- predict_data %>% mutate(year = year + eps)
predict_data_m_eps <- predict_data %>% mutate(year = year - eps)
# Generate posterior simulations from the GS model
n_sim <- 250
set.seed(42)
sim_lp_GS <- predict(gam_model_GS, newdata = predict_data, type = "lpmatrix")
sim_coef_GS <- rmvnorm(n_sim, coef(gam_model_GS), vcov(gam_model_GS, unconditional = TRUE))
# Calculate predicted values and derivatives for the GS model
pred_original_GS <- exp(sim_lp_GS %*% t(sim_coef_GS))
pred_p_eps_GS <- exp(predict(gam_model_GS, newdata = predict_data_p_eps, type = "lpmatrix") %*% t(sim_coef_GS))
pred_m_eps_GS <- exp(predict(gam_model_GS, newdata = predict_data_m_eps, type = "lpmatrix") %*% t(sim_coef_GS))
first_derivative_GS <- (pred_p_eps_GS - pred_m_eps_GS) / (2 * eps)
per_capita_rate_GS <- first_derivative_GS / (pred_original_GS + 1e-9)
# Reshape simulation results for the GS model
sim_deriv_long_GS <- as.data.frame(first_derivative_GS) %>%
mutate(row = 1:n()) %>%
pivot_longer(-row, names_to = "sim_id", values_to = "derivative")
sim_per_capita_long_GS <- as.data.frame(per_capita_rate_GS) %>%
mutate(row = 1:n()) %>%
pivot_longer(-row, names_to = "sim_id", values_to = "per_capita_rate")
sim_results_GS <- predict_data %>%
mutate(row = 1:n()) %>%
left_join(sim_deriv_long_GS, by = "row") %>%
left_join(sim_per_capita_long_GS, by = c("row", "sim_id"))
# Calculate community indicators for the GS model
community_indicators_GS <- sim_results_GS %>%
group_by(year, sim_id) %>%
summarise(
mean_rate_of_change = mean(derivative, na.rm = TRUE),
mean_per_capita_rate = mean(per_capita_rate, na.rm = TRUE),
sd_per_capita_rate = sd(per_capita_rate, na.rm = TRUE),
.groups = 'drop'
)
# Final summary of indicators for the GS model
final_indicators_GS <- community_indicators_GS %>%
group_by(year) %>%
summarise(
across(
.cols = c(mean_rate_of_change, mean_per_capita_rate, sd_per_capita_rate),
.fns = list(
median = ~median(.x, na.rm = TRUE),
lower_ci = ~quantile(.x, 0.025, na.rm = TRUE),
upper_ci = ~quantile(.x, 0.975, na.rm = TRUE)
),
.names = "{.col}_{.fn}"
),
.groups = 'drop'
) %>%
mutate(model_type = "GS Model") # Add a label for plotting3.4.1 Indicators from model GS
HGAMs offer an indicator-based approach using nonparametric spatiotemporal regression models to identify periods of change in community abundance or composition (i.e., regime shifts). This method estimates three key indicators: 1) the mean rate of change across all species, 2) the mean per-capita rate of change, and 3) the standard deviation of per-capita rates of change (Pedersen et al., 2020).
The mean rate of change across all species
This indicator represents the average temporal rate of change in abundance across all species in the community. It provides a general measure of whether the community as a whole is increasing or decreasing in total abundance over time.
The mean per-capita rate of change
This indicator expresses the average rate of change per individual, capturing the community’s relative growth or decline independently of overall abundance. It is analogous to the population growth rate at the individual level and reflects how efficiently individuals contribute to population change through time.
The standard deviation of per-capita rates of change
This indicator quantifies the variability in per-capita rates of change among species. High values suggest that species respond differently to environmental or ecological drivers, indicating potential desynchronization or restructuring within the community, which can signal the onset of regime shifts.
(head(final_indicators_GS))# A tibble: 6 × 11
year mean_rate_of_change_median mean_rate_of_change_…¹ mean_rate_of_change_…²
<int> <dbl> <dbl> <dbl>
1 1978 1.91 -0.402 4.12
2 1979 1.84 -0.367 3.93
3 1980 1.68 -0.0327 3.27
4 1981 1.37 0.137 2.43
5 1982 1.10 -0.0447 2.40
6 1983 0.911 -0.291 2.12
# ℹ abbreviated names: ¹mean_rate_of_change_lower_ci,
# ²mean_rate_of_change_upper_ci
# ℹ 7 more variables: mean_per_capita_rate_median <dbl>,
# mean_per_capita_rate_lower_ci <dbl>, mean_per_capita_rate_upper_ci <dbl>,
# sd_per_capita_rate_median <dbl>, sd_per_capita_rate_lower_ci <dbl>,
# sd_per_capita_rate_upper_ci <dbl>, model_type <chr>
3.5 Step 5: Plot the indicators
Here, we plot the three derivative-based indicators (mean rate of change, mean per capita rate, and the standard deviation of per capita rates) across years.
# Plot 1: Mean Rate of Change
plot1_mean_rof <- ggplot(final_indicators_GS,
aes(x = year)) +
geom_ribbon(aes(ymin = mean_rate_of_change_lower_ci,
ymax = mean_rate_of_change_upper_ci),
alpha = 0.8, fill = "#8fbcbb") +
geom_line(aes(y = mean_rate_of_change_median), linewidth = 1) +
geom_hline(yintercept = 0, linetype = "dashed") +
labs(
title = "",
y = "Mean rate of change\n(Abundance / Year)", x = "Year",
) +
ggpubr::theme_pubr() +
theme(panel.grid.major = element_line(linewidth = .3))
# Plot 2: Mean Per-Capita Rate of Change
plot2_mean_percap_rof <- ggplot(final_indicators_GS,
aes(x = year)) +
geom_ribbon(aes(ymin = mean_per_capita_rate_lower_ci,
ymax = mean_per_capita_rate_upper_ci),
alpha = 0.8, fill = "#88c0d0") +
geom_line(aes(y = mean_per_capita_rate_median), linewidth = 1) +
geom_hline(yintercept = 0, linetype = "dashed") +
labs(
title = "",
y = "Mean per-capita\nrate of change", x = "Year",
) +
ggpubr::theme_pubr() +
theme(panel.grid.major = element_line(linewidth = .3))
# Plot 3: SD of Per-Capita Rates
plot3_SD_percap_rof <- ggplot(final_indicators_GS,
aes(x = year)) +
geom_ribbon(aes(ymin = sd_per_capita_rate_lower_ci,
ymax = sd_per_capita_rate_upper_ci),
alpha = 0.6, fill = "#5e81ac") +
geom_line(aes(y = sd_per_capita_rate_median), linewidth = 1) +
geom_hline(yintercept = 0, linetype = "dashed") +
labs(
title = "",
y = "SD of per-capita\nrates of change", x = "Year",
) +
ggpubr::theme_pubr()+
theme(panel.grid.major = element_line(linewidth = .3))
# Print the plots
print(plot1_mean_rof)print(plot2_mean_percap_rof)print(plot3_SD_percap_rof)3.5.1 Making a figure with the plots of indicators
Here, we create the figure that displays the three derivative-based indicators. This figure corresponds to Box 1 in the paper (i.e., Figure 3).
library(patchwork)
plot1_mean_rof + plot2_mean_percap_rof + plot3_SD_percap_rof + plot_annotation(tag_levels = "a")3.6 Additional material from the “Trends” section
Here, we present additional code developed for the Trends section of the paper that was not included in the final version of the manuscript. This material complements the analyses presented in Box 1.
3.6.1 Plotting the species-specific trends from the GS Model
Here, we plot the species-specific trends estimated from the GS model.
# Get predictions from the GS model
preds_GS <- predict(gam_model_GS, newdata = predict_data, type = "response", se.fit = TRUE)
plot_data_GS <- predict_data %>%
mutate(
fit = preds_GS$fit,
se = preds_GS$se.fit,
lower_ci = fit - 1.96 * se,
upper_ci = fit + 1.96 * se
) %>%
left_join(community_ts_subset, by = c("year", "species"))
# Plot trends from GS model
species_trends_plot_GS <- ggplot(plot_data_GS, aes(x = year)) +
geom_point(aes(y = abundance), color = "grey60", alpha = 0.8) +
geom_ribbon(aes(ymin = lower_ci, ymax = upper_ci), fill = "darkorange", alpha = 0.3) +
geom_line(aes(y = fit), color = "darkorange", size = 1) +
facet_wrap(~ species, scales = "free_y") +
labs(
title = "Fitted Abundance Trends for Each Species (GS Model)",
y = "Predicted Abundance", x = "Year"
) +
theme_minimal()Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.
print(species_trends_plot_GS)3.6.2 Fitting Model “S” and comparing with Model “GS”
Before selecting the GS model as the main example in the Box 1 of the article, we also fitted the S model (Pedersen et al., 2019) and compared the performance of the two models.
The code used for this comparison is provided below.
3.6.2.1 Step 1: Fit Model “S”
Here, we fit the model using the same data subset that was previously used for the GS model. Since the response variable represents abundance (count) data, we use the Poisson family.
# The 'S' Model (Separate smooths for each species)
gam_model_S <- gam(
abundance ~ species +
s(year, by = species, bs = "fs") + # Species-specific smoother: a factor-smoother interaction of year and species
s(species, bs = "re"), # Species as random effects (gives an intercept per species)
data = community_ts_subset,
family = poisson(), # Using Poisson family
method = "REML"
)3.6.2.2 Step 2: Derivatives and Indicators (model S)
In this section, we generate predictions and calculate community-level indicators from the fitted S model. We first create a prediction dataset covering all species and years, and use a small value (ε) to approximate derivatives numerically. We then draw 250 posterior simulations from the model coefficients to account for parameter uncertainty. Using these simulations, we compute predicted abundances and their first derivatives, which are used to estimate per capita rates of change. Finally, we summarize these results to obtain three community indicators for each year: the mean rate of change, the mean per capita rate of change, and the standard deviation of per capita rates of change, along with their median and 95% confidence intervals.
# Create a prediction dataset
predict_data <- community_ts_subset %>%
select(year, species) %>%
distinct()
# Define a small number 'eps' for numerical differentiation
eps <- 1e-7
predict_data_p_eps <- predict_data %>% mutate(year = year + eps)
predict_data_m_eps <- predict_data %>% mutate(year = year - eps)
# Generate posterior simulations from the S model
n_sim <- 250
set.seed(42)
sim_lp_S <- predict(gam_model_S, newdata = predict_data, type = "lpmatrix")
sim_coef_S <- rmvnorm(n_sim, coef(gam_model_S), vcov(gam_model_S, unconditional = TRUE))
# Calculate predicted values and derivatives for the S model
pred_original_S <- exp(sim_lp_S %*% t(sim_coef_S))
pred_p_eps_S <- exp(predict(gam_model_S, newdata = predict_data_p_eps, type = "lpmatrix") %*% t(sim_coef_S))
pred_m_eps_S <- exp(predict(gam_model_S, newdata = predict_data_m_eps, type = "lpmatrix") %*% t(sim_coef_S))
first_derivative_S <- (pred_p_eps_S - pred_m_eps_S) / (2 * eps)
per_capita_rate_S <- first_derivative_S / (pred_original_S + 1e-9)
# Reshape simulation results for the S model
sim_deriv_long_S <- as.data.frame(first_derivative_S) %>%
mutate(row = 1:n()) %>%
pivot_longer(-row, names_to = "sim_id", values_to = "derivative")
sim_per_capita_long_S <- as.data.frame(per_capita_rate_S) %>%
mutate(row = 1:n()) %>%
pivot_longer(-row, names_to = "sim_id", values_to = "per_capita_rate")
sim_results_S <- predict_data %>%
mutate(row = 1:n()) %>%
left_join(sim_deriv_long_S, by = "row") %>%
left_join(sim_per_capita_long_S, by = c("row", "sim_id"))
# Calculate community indicators for the S model
community_indicators_S <- sim_results_S %>%
group_by(year, sim_id) %>%
summarise(
mean_rate_of_change = mean(derivative, na.rm = TRUE),
mean_per_capita_rate = mean(per_capita_rate, na.rm = TRUE),
sd_per_capita_rate = sd(per_capita_rate, na.rm = TRUE),
.groups = 'drop'
)
# Final summary of indicators for the S model
final_indicators_S <- community_indicators_S %>%
group_by(year) %>%
summarise(
across(
.cols = c(mean_rate_of_change, mean_per_capita_rate, sd_per_capita_rate),
.fns = list(
median = ~median(.x, na.rm = TRUE),
lower_ci = ~quantile(.x, 0.025, na.rm = TRUE),
upper_ci = ~quantile(.x, 0.975, na.rm = TRUE)
),
.names = "{.col}_{.fn}"
),
.groups = 'drop'
) %>%
mutate(model_type = "S Model") # Add a label for plotting3.6.2.2.1 Indicators from model S
print(head(final_indicators_S))# A tibble: 6 × 11
year mean_rate_of_change_median mean_rate_of_change_…¹ mean_rate_of_change_…²
<int> <dbl> <dbl> <dbl>
1 1978 0.639 0.0162 1.23
2 1979 0.648 0.0409 1.21
3 1980 0.656 0.110 1.17
4 1981 0.652 0.0905 1.13
5 1982 0.647 0.137 1.09
6 1983 0.624 0.175 1.06
# ℹ abbreviated names: ¹mean_rate_of_change_lower_ci,
# ²mean_rate_of_change_upper_ci
# ℹ 7 more variables: mean_per_capita_rate_median <dbl>,
# mean_per_capita_rate_lower_ci <dbl>, mean_per_capita_rate_upper_ci <dbl>,
# sd_per_capita_rate_median <dbl>, sd_per_capita_rate_lower_ci <dbl>,
# sd_per_capita_rate_upper_ci <dbl>, model_type <chr>
3.6.2.3 Step 3: Plot and compare indicators from both models
Here, we compare each of the three derivative-based indicators obtained from the GS and S models.
# Combine the indicator results from both models into one dataframe
combined_indicators <- bind_rows(final_indicators_S, final_indicators_GS)
# Plot 1: Mean Rate of Change Comparison
plot1_compare <- ggplot(combined_indicators, aes(x = year, group = model_type)) +
geom_ribbon(aes(ymin = mean_rate_of_change_lower_ci, ymax = mean_rate_of_change_upper_ci, fill = model_type), alpha = 0.2) +
geom_line(aes(y = mean_rate_of_change_median, color = model_type), linewidth = 1) +
geom_hline(yintercept = 0, linetype = "dashed") +
labs(
title = "Comparison: Mean Rate of Change",
y = "Mean Rate of Change (Abundance / Year)", x = "Year",
color = "Model Type", fill = "Model Type"
) +
theme_minimal()
# Plot 2: Mean Per-Capita Rate of Change Comparison
plot2_compare <- ggplot(combined_indicators, aes(x = year, group = model_type)) +
geom_ribbon(aes(ymin = mean_per_capita_rate_lower_ci, ymax = mean_per_capita_rate_upper_ci, fill = model_type), alpha = 0.2) +
geom_line(aes(y = mean_per_capita_rate_median, color = model_type), size = 1) +
geom_hline(yintercept = 0, linetype = "dashed") +
labs(
title = "Comparison: Mean Per-Capita Rate of Change",
y = "Mean Per-Capita Rate (Year⁻¹)", x = "Year",
color = "Model Type", fill = "Model Type"
) +
theme_minimal()
# Plot 3: SD of Per-Capita Rates Comparison
plot3_compare <- ggplot(combined_indicators, aes(x = year, group = model_type)) +
geom_ribbon(aes(ymin = sd_per_capita_rate_lower_ci, ymax = sd_per_capita_rate_upper_ci, fill = model_type), alpha = 0.2) +
geom_line(aes(y = sd_per_capita_rate_median, color = model_type), size = 1) +
geom_hline(yintercept = 0, linetype = "dashed") +
labs(
title = "Comparison: SD of Per-Capita Rates of Change",
y = "SD of Per-Capita Rates (Year⁻¹)", x = "Year",
color = "Model Type", fill = "Model Type"
) +
theme_minimal()
# Print the comparison plots
print(plot1_compare)print(plot2_compare)print(plot3_compare)3.6.2.4 Step 4: Comparing the models (AIC)
Here, we compare the GS and S models using the Akaike Information Criterion (AIC).
# Compare the models using AIC
aic_S <- AIC(gam_model_S)
aic_GS <- AIC(gam_model_GS)
# Print the results for comparison
print(paste("AIC for Poisson S Model:", round(aic_S, 2)))[1] "AIC for Poisson S Model: 7157.55"
print(paste("AIC for Poisson GS Model:", round(aic_GS, 2)))[1] "AIC for Poisson GS Model: 7097.81"
# Best AIC score: Model GS3.6.2.5 Step 5 (additional step): Plotting the species-specific trends from model S
Here, we plot the species-specific trends estimated from the S model.
# Get predictions from the S model
preds_S <- predict(gam_model_S, newdata = predict_data, type = "response", se.fit = TRUE)
plot_data_S <- predict_data %>%
mutate(
fit = preds_S$fit,
se = preds_S$se.fit,
lower_ci = fit - 1.96 * se,
upper_ci = fit + 1.96 * se
) %>%
left_join(community_ts_subset, by = c("year", "species"))
# Plot trends from S model
species_trends_plot_S <- ggplot(plot_data_S, aes(x = year)) +
geom_point(aes(y = abundance), color = "grey60", alpha = 0.8) +
geom_ribbon(aes(ymin = lower_ci, ymax = upper_ci), fill = "steelblue", alpha = 0.3) +
geom_line(aes(y = fit), color = "steelblue", size = 1) +
facet_wrap(~ species, scales = "free_y") +
labs(
title = "Fitted Abundance Trends for Each Species (S Model)",
y = "Predicted Abundance", x = "Year"
) +
theme_minimal()
print(species_trends_plot_S)4 Supplementary Material 3 - Boxes 2 & 3
In this section, we present the coding examples from Boxes 2 (Variance) and 3 (Prediction), both of which use the same data subset (d_crop) from Waverly, New York.
4.1 Step 1: Setting up the work environment
4.1.1 Make a subset of the data (d_crop)
The dataset is cropped to include only observations from the Waverly, New York region, and the Red-eyed vireo (Vireo olivaceus) is removed due to inconsistent data.
df = df |>
select(-c(SAMPLE_DESC, DAY, MONTH, BIOMAS))
sites = paste0(df$LONGITUDE,"_", df$LATITUDE)
table(sites)sites
-100.483_37.3167 -102.25_35.7333 -103.367_47.2167 -103.633_43.8167
988 1170 1201 1233
-103.667_39.8667 -105.067_40.5 -105.65_52.7333 -105.733_42.8167
696 1364 1142 818
-105.8_36.0833 -105.85_53.1 -106.067_35.5167 -106.117_42.8667
1700 1197 1044 1241
-106.117_51.4 -106.717_44.8833 -107.667_39.9833 -107.85_52.25
936 1127 1604 1518
-107.983_38.3 -108.967_31.8333 -109.45_45.7 -110.3_32.0333
1497 871 1755 1466
-110.8_31.5167 -111.8_45.8833 -111.85_50.5667 -112.267_44.2333
1834 1411 968 714
-112.383_34.6667 -112.483_42.85 -112.8_43.15 -113.367_44.7833
2064 979 1018 1124
-113.467_43.4167 -113.567_45 -113.65_46.7 -114.167_47.7
867 1325 1272 1216
-114.217_44.55 -114.467_48.1167 -114.483_52.0167 -114.75_54.0833
1155 1809 1333 1383
-115.15_47.3667 -115.617_40.0667 -117.217_45.2833 -118.133_36.5
1326 819 1338 1106
-118.333_49.9833 -118.5_48.05 -119.283_36.65 -119.367_37.3
1639 1635 1627 1600
-119.717_49.6 -119.733_48.0833 -120.25_40.85 -120.45_38.85
2124 1059 1084 1580
-120.667_51.4 -120.833_37.5833 -120.85_39.5667 -120.933_38.75
1458 1159 1421 1762
-121.017_39.05 -121.1_41.8333 -121.217_48.75 -121.267_41.1
1415 1149 1553 1762
-121.583_40.8 -121.583_46.35 -121.617_39.6 -121.667_36.45
1313 1550 1101 1908
-121.8_42.3667 -121.9_41.9833 -122.067_39.55 -122.067_52.1667
1363 1394 944 1399
-122.15_41.85 -122.25_39.7667 -122.3_40.8833 -122.333_48.1333
2047 973 1437 1461
-122.667_41.75 -122.717_38.5667 -122.8_53.9333 -123.067_41.9167
1752 1632 1477 1576
-123.233_42.9333 -123.383_48.1167 -123.5_43.35 -123.617_38.8
1598 1538 1725 1969
-123.667_42.4167 -124.4_42.5167 -124.667_48.1167 -61.5667_45.15
1637 1124 1207 1397
-62.6_44.9333 -65.7167_45.6333 -65.95_45.7167 -68.9167_47.9333
1365 2081 1702 1784
-69.45_44.9833 -69.5667_43.9833 -70.5333_43.5 -70.5667_44.15
1616 1568 1813 1796
-70.6167_47.65 -70.6667_43.25 -70.7167_43.15 -70.9167_43.2333
1243 1378 1253 1752
-71.1333_46.0167 -71.3_43.2 -71.3667_45 -71.4667_46.7
1662 1741 1848 1477
-71.5667_44.7 -71.7167_44.1667 -71.75_43.3667 -71.8667_42.8833
1732 2074 1674 1771
-71.9333_43.4333 -72.1333_41.7667 -72.1667_42.8 -72.2_43.0667
1803 1694 1890 1886
-72.2833_42.6167 -72.35_42.2667 -72.4_43.0167 -72.4667_42.2167
1909 1833 1742 1876
-72.5167_41.7 -72.5833_45.95 -72.85_42.35 -72.9_42.4667
1489 1632 1937 1894
-73.1833_42.4167 -73.2167_41.55 -73.3333_41.75 -73.3333_45.0833
1708 1824 2084 1214
-73.4_45.7167 -73.4167_42.1 -73.5_41.5333 -73.5_42.3333
1606 2075 1869 1732
-73.9833_41.75 -74.0667_45.7833 -74.1833_44.45 -74.3333_41.9833
1697 1907 1787 1928
-74.4833_44.55 -74.9167_40.4667 -75.1_40.6667 -75.1167_39.5
1847 1673 1532 1351
-75.2333_41.55 -75.25_38.2333 -75.25_41.35 -75.3667_40.8167
2099 1744 1990 1319
-75.4667_39.0333 -75.4667_40.15 -75.5333_38.95 -75.5833_38.1667
1561 1405 1861 1732
-75.6833_39.5 -75.7667_39.2667 -75.7833_38.55 -75.7833_41.7
1615 1886 1713 1905
-75.8833_38.7833 -75.9_43.45 -75.9167_39.5167 -75.9333_38.8833
1712 1831 1815 1769
-75.9333_42.35 -75.9667_40.8167 -76_39.6167 -76.0167_46.35
1752 1904 1879 1719
-76.0333_42.35 -76.1_45.5667 -76.15_39.2667 -76.1667_38.2667
1692 1810 1818 1923
-76.1833_39.1 -76.2167_38.5333 -76.25_38.4667 -76.2833_36.6167
1902 1978 1583 1631
-76.3_39.45 -76.4333_41.2167 -76.4833_39.5333 -76.5167_41.1
1595 1944 1533 1838
-76.6333_42.55 -76.6667_34.95 -76.6833_37.8667 -76.7167_40.2
1690 1883 1750 1434
-76.7333_39.7 -76.8167_39.55 -76.85_39.0167 -76.9667_38.4833
1741 1649 1556 1723
-76.9667_39.7333 -76.9833_36.35 -77.0333_39.5167 -77.0333_39.65
1809 2020 1708 1709
-77.05_38.6 -77.0667_44.35 -77.0833_38.6333 -77.0833_39.15
1784 2505 1674 1996
-77.1167_42.9 -77.1667_41.6667 -77.35_44.0667 -77.4_40.5833
1812 1689 1586 1603
-77.4167_35.9833 -77.4667_45.2833 -77.5167_40.6833 -77.55_39.5833
1875 1752 1600 1929
-77.7167_35.3 -77.85_39.65 -77.85_42.5 -77.95_42.2
1588 1721 2096 1843
-77.95_42.7 -77.9833_36.25 -78.0833_42.6167 -78.1833_40.5833
1765 1956 1573 1727
-78.3667_42.6 -78.4833_39.1833 -78.55_38.55 -78.5667_38.8167
1432 1769 1605 1559
-78.5833_42.0833 -78.6833_37.9 -78.8_37.7 -78.8167_39.6167
1583 1906 1837 1848
-78.8333_42.0667 -78.9667_39.7833 -78.9833_43.25 -79_41.6167
1885 1840 1550 1568
-79.0667_39.8833 -79.1333_39.4333 -79.15_38.2 -79.1833_44.3167
1845 2015 1699 1729
-79.2333_40.6667 -79.25_39.2167 -79.25_40.6333 -79.35_41.5167
1847 1552 1814 1672
-79.6333_37.65 -79.65_39.65 -79.75_43.55 -79.8333_39.6
1570 1506 1655 1427
-79.9333_39.0833 -80.05_37.7833 -80.3333_38.7167 -80.35_40.1667
1626 1683 1633 1683
-80.75_39.9333 -80.7833_39.65 -80.7833_41.6333 -80.9167_43.15
1811 1928 1657 1386
-80.9833_41.3167 -81.2167_44.3 -81.3833_27.3 -81.4833_26.3
1568 1302 1149 855
-81.7333_32.5833 -81.8_38.5667 -81.8_45.7167 -81.8167_29.8333
1525 1728 1801 1252
-81.8833_39.2667 -81.95_37.0167 -81.9833_28.55 -82.15_27.6667
1644 1436 1228 1154
-82.1667_39.3333 -82.2167_33.5167 -82.25_30.2 -82.2833_39.25
1628 1652 1280 1680
-82.3_28.3167 -82.5_37.2333 -82.6333_33.65 -83.2833_34.65
1349 1841 1739 1734
-83.4167_38.6667 -83.4833_32.4 -83.5833_33.6 -83.8167_33.1
1787 1558 1710 1587
-83.8833_30.65 -83.9167_30.1833 -83.95_38.2167 -84.0333_30.5833
1503 1529 1778 1389
-84.15_35.9167 -84.1667_38.4333 -84.2167_33.6333 -84.2833_32.2
1496 1623 1649 1529
-84.3167_36.5333 -84.35_46.2167 -84.3667_36.0667 -84.4167_36.2833
1875 1562 1950 2026
-84.4167_41.8167 -84.6_38.3667 -84.75_37.3333 -84.85_40.6833
1519 1691 1660 1340
-84.9_29.9833 -85.1333_37.4333 -85.25_33.5333 -85.3_29.7833
1232 1981 1729 1289
-85.35_35.1 -85.4167_42.25 -85.55_32.3 -85.65_35.1833
1728 1759 1599 1731
-85.7667_36.1 -85.7667_41.9667 -85.9167_35.3833 -86.1333_42.5167
1823 1671 1581 1983
-86.1833_35.7333 -86.2333_34.8667 -86.2333_43.8833 -86.25_31.5833
1816 1337 1587 1510
-86.6_31.45 -86.6_33.4667 -86.6167_36.9667 -86.65_36.5
1731 1811 1637 1484
-86.6667_35.3333 -86.8333_35.8333 -87_33.5333 -87.1_33.1333
1624 1499 1740 1562
-87.15_39.5667 -87.2_31.75 -87.2167_32.45 -87.3333_35.8667
1368 1700 1663 2014
-87.35_40.6667 -87.5333_32.7833 -87.6833_35.4833 -87.7333_40.65
1581 1729 2007 1255
-87.7833_39.3333 -87.8833_43.35 -87.8833_45.3667 -87.9833_42.7833
1282 1614 2036 1431
-88.0333_42.6333 -88.1_39.9 -88.1667_44.8667 -88.1833_41.1667
1662 1291 2344 873
-88.2_33.4833 -88.2_36.7 -88.2_39.3167 -88.2333_38.2167
1765 1719 1548 1558
-88.2667_39.3667 -88.3333_32.15 -88.35_43.6667 -88.3833_39.6167
1157 1756 1640 1220
-88.5167_31.6667 -88.5167_37.0667 -88.5333_35.3833 -88.55_40.0833
1338 1988 1496 1088
-88.6833_44.05 -88.75_45.4833 -88.8_35.3667 -88.8_44.6167
1984 2102 1629 1994
-88.95_37.3167 -88.95_40.9333 -88.95_44.4167 -89.0167_41.65
1853 1106 2476 1030
-89.0333_44.2 -89.0833_35.3667 -89.0833_42.0667 -89.1833_43.55
1805 1657 1467 1936
-89.1833_45.9333 -89.2_39.4 -89.25_37.2333 -89.2833_44.7333
2029 1061 1937 1728
-89.3333_35.6833 -89.3333_42.1667 -89.3667_35.55 -89.3667_36.3
1371 1625 1297 1437
-89.4333_36.4167 -89.45_39.55 -89.45_41.2 -89.5167_37.3
1743 1240 1268 1454
-89.6167_45.3167 -89.6333_40.6 -89.6333_46.1833 -89.75_37.9667
1985 1384 1812 1787
-89.8_40.9333 -89.8167_38.5333 -89.8833_43.4333 -90.0333_40.9167
1307 1592 1851 1472
-90.05_44.6167 -90.0667_45.3333 -90.1667_39.4333 -90.2_45.6333
1313 1893 1604 2117
-90.3_41.9667 -90.3167_43.7333 -90.3667_44.2167 -90.3833_44.8
1454 1841 1833 1702
-90.45_37.25 -90.5_34.9333 -90.5_40.8667 -90.5833_42.05
1968 1288 1053 1433
-90.6667_35.5333 -90.6833_47.7333 -90.95_46.8333 -90.9833_40.65
1202 1289 1963 1616
-91.0667_46.3 -91.1833_40.2167 -91.35_35.9 -91.4167_44.0167
1793 1503 1438 1735
-91.45_37.9 -91.5_47.6833 -91.5833_37.3667 -91.8_47.0667
1740 1440 1837 1676
-91.8333_30.0667 -92.2_35.5667 -92.2333_46.3167 -92.25_45.6333
1081 1654 2121 2118
-92.45_38.5667 -92.5_45.9667 -92.6333_34.35 -92.7_33.5833
1716 1581 1829 1786
-92.7_45.3833 -92.7167_35.6333 -92.85_38.2833 -92.8667_40.65
1931 1694 1861 1444
-93.0667_35.8167 -93.15_40.8833 -93.25_34.05 -93.2833_36.1
1579 1370 1730 1785
-93.3333_44.65 -93.4667_44.9667 -93.4833_33.3667 -93.5_43.8167
1508 1546 1648 1177
-93.5_45.5667 -93.5167_37.45 -93.6_35.4167 -93.6333_47.3333
1827 1499 1602 1481
-93.6833_33.6667 -94.0167_43.2 -94.0667_34.9833 -94.0833_41.75
1552 1152 1044 1307
-94.1167_36.4 -94.1167_37.15 -94.1333_33.7 -94.2_45.1667
1442 1452 1522 1531
-94.25_49.7167 -94.5167_31.8833 -94.85_31.1833 -94.8667_35.8167
1866 1663 1504 2069
-94.9_38.8 -94.9333_30.7 -95.1333_36.9167 -95.4667_46.75
1589 1462 1380 1763
-95.6_39.25 -95.6167_28.9 -95.6167_39.05 -95.7833_38.45
1414 1136 1631 1564
-95.8667_31.8 -95.8833_38.9 -96.0167_39.7167 -96.0667_41.1667
1261 1729 1659 1186
-96.0833_41.35 -96.3833_42.4667 -96.5_38.3167 -96.7167_49.7167
1395 1344 1321 1322
-96.7667_38.9167 -96.8833_39.8833 -96.95_44.2333 -97.1833_34.1333
1728 1410 1244 1316
-97.2667_33.55 -97.35_41.1667 -97.4_47.9667 -97.4333_35.1833
1229 971 1607 1667
-97.4667_43.95 -97.7_26.5333 -98.0167_49.3833 -98.05_32.1667
1231 931 1426 1120
-99.1833_30.35 -99.2167_37.2167 -99.5667_39.6833 -99.9833_50.2
1187 1320 985 1167
# crop to a site
d_crop = df[sites %in% "-74.4833_44.55",] # We keep sites in Waverly, New York
## crop to birds
species = table(d_crop$valid_name)
species = species[which(species == 30)]
ex = names(species)
d_crop = dplyr::filter(d_crop, valid_name %in% ex)
d_crop = dplyr::filter(d_crop, valid_name != "Vireo olivaceus")4.2 Step 2: Data exploration
# summarise data contents
dls = d_crop |>
group_by(valid_name) |>
group_split()
# check for basic population trends
mls = lapply(dls, function(x){lm(ABUNDANCE ~ YEAR, data = x)})
# extract slopes
coefs = mls |> lapply(coef) |>
bind_rows() |>
mutate("species" = unique(d_crop$valid_name))
# plot to see the slopes
ggplot(data = coefs) +
geom_point(aes(y = species, x = YEAR))4.3 Step 3: Box 2 - Variance
4.3.1 Build a model for each species
# check for basic population trends
gamls = lapply(dls, function(x){gam(ABUNDANCE ~ s(YEAR, k = 4), data = x)})
lapply(gamls, plot)[[1]]
[[1]][[1]]
[[1]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[1]][[1]]$scale
[1] TRUE
[[1]][[1]]$se
[1] 11.917084 11.301201 10.695914 10.103460 9.526369 8.967671 8.430857
[8] 7.919777 7.438676 6.992187 6.585134 6.222323 5.908240 5.646592
[15] 5.439779 5.288406 5.190961 5.143721 5.141007 5.175787 5.240271
[22] 5.326468 5.426800 5.534432 5.643283 5.748147 5.844854 5.929987
[29] 6.000775 6.055263 6.092139 6.110505 6.109987 6.090822 6.053571
[36] 5.999125 5.928916 5.844733 5.748622 5.643030 5.530807 5.415024
[43] 5.298980 5.186265 5.080538 4.985402 4.904329 4.840452 4.796325
[50] 4.773776 4.773776 4.796325 4.840452 4.904329 4.985402 5.080538
[57] 5.186265 5.298980 5.415024 5.530807 5.643030 5.748622 5.844733
[64] 5.928916 5.999125 6.053571 6.090822 6.109987 6.110505 6.092139
[71] 6.055263 6.000775 5.929987 5.844854 5.748147 5.643283 5.534432
[78] 5.426800 5.326468 5.240271 5.175787 5.141007 5.143721 5.190961
[85] 5.288406 5.439779 5.646592 5.908240 6.222323 6.585134 6.992187
[92] 7.438676 7.919777 8.430857 8.967671 9.526369 10.103460 10.695914
[99] 11.301201 11.917084
[[1]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[1]][[1]]$xlab
[1] "YEAR"
[[1]][[1]]$ylab
[1] "s(YEAR,2.85)"
[[1]][[1]]$main
NULL
[[1]][[1]]$se.mult
[1] 2
[[1]][[1]]$xlim
[1] 1978 2007
[[1]][[1]]$fit
[,1]
[1,] 7.6407932
[2,] 6.9492547
[3,] 6.2588084
[4,] 5.5705463
[5,] 4.8855848
[6,] 4.2054225
[7,] 3.5318632
[8,] 2.8667195
[9,] 2.2119042
[10,] 1.5695711
[11,] 0.9419096
[12,] 0.3311141
[13,] -0.2605788
[14,] -0.8309116
[15,] -1.3776279
[16,] -1.8985468
[17,] -2.3916013
[18,] -2.8547337
[19,] -3.2859430
[20,] -3.6835075
[21,] -4.0457911
[22,] -4.3711713
[23,] -4.6583154
[24,] -4.9061674
[25,] -5.1136824
[26,] -5.2799729
[27,] -5.4046138
[28,] -5.4872644
[29,] -5.5276259
[30,] -5.5258439
[31,] -5.4823338
[32,] -5.3975175
[33,] -5.2720686
[34,] -5.1071161
[35,] -4.9038370
[36,] -4.6634831
[37,] -4.3877614
[38,] -4.0785501
[39,] -3.7377367
[40,] -3.3674746
[41,] -2.9702223
[42,] -2.5484548
[43,] -2.1047305
[44,] -1.6419081
[45,] -1.1629138
[46,] -0.6706851
[47,] -0.1683110
[48,] 0.3410093
[49,] 0.8540736
[50,] 1.3676566
[51,] 1.8784823
[52,] 2.3832676
[53,] 2.8787398
[54,] 3.3617013
[55,] 3.8289888
[56,] 4.2774421
[57,] 4.7040271
[58,] 5.1058822
[59,] 5.4801584
[60,] 5.8240800
[61,] 6.1351965
[62,] 6.4111476
[63,] 6.6495909
[64,] 6.8485067
[65,] 7.0061577
[66,] 7.1208164
[67,] 7.1909344
[68,] 7.2154404
[69,] 7.1933413
[70,] 7.1236940
[71,] 7.0060287
[72,] 6.8401373
[73,] 6.6258185
[74,] 6.3631495
[75,] 6.0526671
[76,] 5.6949510
[77,] 5.2906676
[78,] 4.8409585
[79,] 4.3471265
[80,] 3.8104859
[81,] 3.2326330
[82,] 2.6154586
[83,] 1.9608678
[84,] 1.2708512
[85,] 0.5476788
[86,] -0.2063224
[87,] -0.9888170
[88,] -1.7973631
[89,] -2.6294481
[90,] -3.4825584
[91,] -4.3542108
[92,] -5.2419819
[93,] -6.1434559
[94,] -7.0562569
[95,] -7.9782824
[96,] -8.9075427
[97,] -9.8420580
[98,] -10.7801849
[99,] -11.7207020
[100,] -12.6624140
[[1]][[1]]$plot.me
[1] TRUE
[[2]]
[[2]][[1]]
[[2]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[2]][[1]]$scale
[1] TRUE
[[2]][[1]]$se
[1] 11.3301747 11.1012822 10.8723898 10.6434974 10.4146050 10.1857126
[7] 9.9568202 9.7279277 9.4990353 9.2701429 9.0412505 8.8123581
[13] 8.5834656 8.3545732 8.1256808 7.8967884 7.6678960 7.4390036
[19] 7.2101111 6.9812187 6.7523263 6.5234339 6.2945415 6.0656491
[25] 5.8367566 5.6078642 5.3789718 5.1500794 4.9211870 4.6922946
[31] 4.4634021 4.2345097 4.0056173 3.7767249 3.5478325 3.3189401
[37] 3.0900476 2.8611552 2.6322628 2.4033704 2.1744780 1.9455856
[43] 1.7166931 1.4878007 1.2589083 1.0300159 0.8011235 0.5722311
[49] 0.3433387 0.1144464 0.1144464 0.3433387 0.5722311 0.8011235
[55] 1.0300159 1.2589083 1.4878007 1.7166931 1.9455856 2.1744780
[61] 2.4033704 2.6322628 2.8611552 3.0900476 3.3189401 3.5478325
[67] 3.7767249 4.0056173 4.2345097 4.4634021 4.6922946 4.9211870
[73] 5.1500794 5.3789718 5.6078642 5.8367566 6.0656491 6.2945415
[79] 6.5234339 6.7523263 6.9812187 7.2101111 7.4390036 7.6678960
[85] 7.8967884 8.1256808 8.3545732 8.5834656 8.8123581 9.0412505
[91] 9.2701429 9.4990353 9.7279277 9.9568202 10.1857126 10.4146050
[97] 10.6434974 10.8723898 11.1012822 11.3301747
[[2]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[2]][[1]]$xlab
[1] "YEAR"
[[2]][[1]]$ylab
[1] "s(YEAR,1)"
[[2]][[1]]$main
NULL
[[2]][[1]]$se.mult
[1] 2
[[2]][[1]]$xlim
[1] 1978 2007
[[2]][[1]]$fit
[,1]
[1,] 3.64516129
[2,] 3.57152166
[3,] 3.49788204
[4,] 3.42424242
[5,] 3.35060280
[6,] 3.27696318
[7,] 3.20332355
[8,] 3.12968393
[9,] 3.05604431
[10,] 2.98240469
[11,] 2.90876507
[12,] 2.83512545
[13,] 2.76148582
[14,] 2.68784620
[15,] 2.61420658
[16,] 2.54056696
[17,] 2.46692734
[18,] 2.39328772
[19,] 2.31964809
[20,] 2.24600847
[21,] 2.17236885
[22,] 2.09872923
[23,] 2.02508961
[24,] 1.95144998
[25,] 1.87781036
[26,] 1.80417074
[27,] 1.73053112
[28,] 1.65689150
[29,] 1.58325188
[30,] 1.50961225
[31,] 1.43597263
[32,] 1.36233301
[33,] 1.28869339
[34,] 1.21505377
[35,] 1.14141414
[36,] 1.06777452
[37,] 0.99413490
[38,] 0.92049528
[39,] 0.84685566
[40,] 0.77321603
[41,] 0.69957641
[42,] 0.62593679
[43,] 0.55229717
[44,] 0.47865755
[45,] 0.40501792
[46,] 0.33137830
[47,] 0.25773868
[48,] 0.18409906
[49,] 0.11045944
[50,] 0.03681981
[51,] -0.03681981
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[53,] -0.18409905
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[56,] -0.40501792
[57,] -0.47865754
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[60,] -0.69957641
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[62,] -0.84685565
[63,] -0.92049527
[64,] -0.99413490
[65,] -1.06777452
[66,] -1.14141414
[67,] -1.21505376
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[78,] -2.02508961
[79,] -2.09872923
[80,] -2.17236885
[81,] -2.24600847
[82,] -2.31964809
[83,] -2.39328772
[84,] -2.46692734
[85,] -2.54056696
[86,] -2.61420658
[87,] -2.68784621
[88,] -2.76148583
[89,] -2.83512545
[90,] -2.90876507
[91,] -2.98240469
[92,] -3.05604432
[93,] -3.12968394
[94,] -3.20332356
[95,] -3.27696318
[96,] -3.35060281
[97,] -3.42424243
[98,] -3.49788205
[99,] -3.57152167
[100,] -3.64516129
[[2]][[1]]$plot.me
[1] TRUE
[[3]]
[[3]][[1]]
[[3]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[3]][[1]]$scale
[1] TRUE
[[3]][[1]]$se
[1] 6.98233708 6.84127976 6.70022245 6.55916513 6.41810782 6.27705050
[7] 6.13599319 5.99493587 5.85387856 5.71282125 5.57176393 5.43070662
[13] 5.28964930 5.14859199 5.00753467 4.86647736 4.72542004 4.58436273
[19] 4.44330541 4.30224810 4.16119078 4.02013347 3.87907615 3.73801884
[25] 3.59696152 3.45590421 3.31484690 3.17378958 3.03273227 2.89167495
[31] 2.75061764 2.60956032 2.46850301 2.32744569 2.18638838 2.04533106
[37] 1.90427375 1.76321643 1.62215912 1.48110180 1.34004449 1.19898718
[43] 1.05792986 0.91687255 0.77581523 0.63475792 0.49370060 0.35264329
[49] 0.21158597 0.07052866 0.07052866 0.21158597 0.35264329 0.49370060
[55] 0.63475792 0.77581523 0.91687255 1.05792986 1.19898718 1.34004449
[61] 1.48110180 1.62215912 1.76321643 1.90427375 2.04533106 2.18638838
[67] 2.32744569 2.46850301 2.60956032 2.75061764 2.89167495 3.03273227
[73] 3.17378958 3.31484690 3.45590421 3.59696152 3.73801884 3.87907615
[79] 4.02013347 4.16119078 4.30224810 4.44330541 4.58436273 4.72542004
[85] 4.86647736 5.00753467 5.14859199 5.28964930 5.43070662 5.57176393
[91] 5.71282125 5.85387856 5.99493587 6.13599319 6.27705050 6.41810782
[97] 6.55916513 6.70022245 6.84127976 6.98233708
[[3]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[3]][[1]]$xlab
[1] "YEAR"
[[3]][[1]]$ylab
[1] "s(YEAR,1)"
[[3]][[1]]$main
NULL
[[3]][[1]]$se.mult
[1] 2
[[3]][[1]]$xlim
[1] 1978 2007
[[3]][[1]]$fit
[,1]
[1,] 11.0677419
[2,] 10.8441512
[3,] 10.6205604
[4,] 10.3969697
[5,] 10.1733790
[6,] 9.9497882
[7,] 9.7261975
[8,] 9.5026067
[9,] 9.2790160
[10,] 9.0554252
[11,] 8.8318345
[12,] 8.6082437
[13,] 8.3846530
[14,] 8.1610622
[15,] 7.9374715
[16,] 7.7138807
[17,] 7.4902900
[18,] 7.2666993
[19,] 7.0431085
[20,] 6.8195178
[21,] 6.5959270
[22,] 6.3723363
[23,] 6.1487455
[24,] 5.9251548
[25,] 5.7015640
[26,] 5.4779733
[27,] 5.2543825
[28,] 5.0307918
[29,] 4.8072010
[30,] 4.5836103
[31,] 4.3600196
[32,] 4.1364288
[33,] 3.9128381
[34,] 3.6892473
[35,] 3.4656566
[36,] 3.2420658
[37,] 3.0184751
[38,] 2.7948843
[39,] 2.5712936
[40,] 2.3477028
[41,] 2.1241121
[42,] 1.9005213
[43,] 1.6769306
[44,] 1.4533399
[45,] 1.2297491
[46,] 1.0061584
[47,] 0.7825676
[48,] 0.5589769
[49,] 0.3353861
[50,] 0.1117954
[51,] -0.1117954
[52,] -0.3353861
[53,] -0.5589769
[54,] -0.7825676
[55,] -1.0061584
[56,] -1.2297491
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[60,] -2.1241121
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[62,] -2.5712936
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[64,] -3.0184751
[65,] -3.2420658
[66,] -3.4656566
[67,] -3.6892473
[68,] -3.9128381
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[70,] -4.3600196
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[72,] -4.8072010
[73,] -5.0307918
[74,] -5.2543825
[75,] -5.4779733
[76,] -5.7015640
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[78,] -6.1487455
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[80,] -6.5959270
[81,] -6.8195178
[82,] -7.0431085
[83,] -7.2666993
[84,] -7.4902900
[85,] -7.7138807
[86,] -7.9374715
[87,] -8.1610622
[88,] -8.3846530
[89,] -8.6082437
[90,] -8.8318345
[91,] -9.0554252
[92,] -9.2790160
[93,] -9.5026067
[94,] -9.7261975
[95,] -9.9497882
[96,] -10.1733790
[97,] -10.3969697
[98,] -10.6205604
[99,] -10.8441512
[100,] -11.0677419
[[3]][[1]]$plot.me
[1] TRUE
[[4]]
[[4]][[1]]
[[4]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[4]][[1]]$scale
[1] TRUE
[[4]][[1]]$se
[1] 14.869908 14.104611 13.352472 12.616253 11.899079 11.204685 10.537376
[8] 9.901887 9.303439 8.747722 8.240658 7.788143 7.395683 7.067843
[15] 6.807606 6.615778 6.490587 6.427564 6.419826 6.458808 6.534969
[22] 6.638484 6.760001 6.891052 7.024086 7.152624 7.271458 7.376320
[29] 7.463737 7.531254 7.577213 7.600475 7.600556 7.577727 7.532667
[36] 7.466463 7.380876 7.278107 7.160672 7.031585 6.894355 6.752755
[43] 6.610840 6.473010 6.343749 6.227461 6.128385 6.050340 5.996436
[50] 5.968893 5.968893 5.996436 6.050340 6.128385 6.227461 6.343749
[57] 6.473010 6.610840 6.752755 6.894355 7.031585 7.160672 7.278107
[64] 7.380876 7.466463 7.532667 7.577727 7.600556 7.600475 7.577213
[71] 7.531254 7.463737 7.376320 7.271458 7.152624 7.024086 6.891052
[78] 6.760001 6.638484 6.534969 6.458808 6.419826 6.427564 6.490587
[85] 6.615778 6.807606 7.067843 7.395683 7.788143 8.240658 8.747722
[92] 9.303439 9.901887 10.537376 11.204685 11.899079 12.616253 13.352472
[99] 14.104611 14.869908
[[4]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[4]][[1]]$xlab
[1] "YEAR"
[[4]][[1]]$ylab
[1] "s(YEAR,2.83)"
[[4]][[1]]$main
NULL
[[4]][[1]]$se.mult
[1] 2
[[4]][[1]]$xlim
[1] 1978 2007
[[4]][[1]]$fit
[,1]
[1,] -23.19877967
[2,] -23.10036369
[3,] -23.00086500
[4,] -22.89920090
[5,] -22.79426504
[6,] -22.68457746
[7,] -22.56835993
[8,] -22.44382561
[9,] -22.30909475
[10,] -22.16206341
[11,] -22.00059458
[12,] -21.82254909
[13,] -21.62576959
[14,] -21.40808958
[15,] -21.16734425
[16,] -20.90146366
[17,] -20.60852057
[18,] -20.28659951
[19,] -19.93385001
[20,] -19.54874164
[21,] -19.12984225
[22,] -18.67573494
[23,] -18.18532628
[24,] -17.65783206
[25,] -17.09248059
[26,] -16.48867355
[27,] -15.84632254
[28,] -15.16543244
[29,] -14.44605351
[30,] -13.68872171
[31,] -12.89426765
[32,] -12.06352893
[33,] -11.19761545
[34,] -10.29812981
[35,] -9.36672651
[36,] -8.40514008
[37,] -7.41559144
[38,] -6.40048429
[39,] -5.36223203
[40,] -4.30352708
[41,] -3.22738122
[42,] -2.13682371
[43,] -1.03496792
[44,] 0.07476943
[45,] 1.18890326
[46,] 2.30393841
[47,] 3.41624081
[48,] 4.52207515
[49,] 5.61770376
[50,] 6.69938080
[51,] 7.76334253
[52,] 8.80582283
[53,] 9.82307237
[54,] 10.81146865
[55,] 11.76744713
[56,] 12.68744745
[57,] 13.56807913
[58,] 14.40618485
[59,] 15.19862416
[60,] 15.94235001
[61,] 16.63472969
[62,] 17.27324538
[63,] 17.85540121
[64,] 18.37910212
[65,] 18.84260326
[66,] 19.24417194
[67,] 19.58229447
[68,] 19.85604008
[69,] 20.06457387
[70,] 20.20712129
[71,] 20.28348065
[72,] 20.29376688
[73,] 20.23810290
[74,] 20.11694623
[75,] 19.93130587
[76,] 19.68224237
[77,] 19.37091969
[78,] 18.99906722
[79,] 18.56860654
[80,] 18.08147267
[81,] 17.53993234
[82,] 16.94659921
[83,] 16.30410332
[84,] 15.61517320
[85,] 14.88285814
[86,] 14.11027257
[87,] 13.30053996
[88,] 12.45689347
[89,] 11.58263923
[90,] 10.68108430
[91,] 9.75548591
[92,] 8.80900217
[93,] 7.84477947
[94,] 6.86591019
[95,] 5.87512104
[96,] 4.87498705
[97,] 3.86807059
[98,] 2.85649611
[99,] 1.84183940
[100,] 0.82564158
[[4]][[1]]$plot.me
[1] TRUE
[[5]]
[[5]][[1]]
[[5]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[5]][[1]]$scale
[1] TRUE
[[5]][[1]]$se
[1] 4.15484109 4.07090491 3.98696873 3.90303254 3.81909636 3.73516018
[7] 3.65122399 3.56728781 3.48335163 3.39941544 3.31547926 3.23154307
[13] 3.14760689 3.06367071 2.97973452 2.89579834 2.81186216 2.72792597
[19] 2.64398979 2.56005360 2.47611742 2.39218124 2.30824505 2.22430887
[25] 2.14037269 2.05643650 1.97250032 1.88856413 1.80462795 1.72069177
[31] 1.63675558 1.55281940 1.46888322 1.38494703 1.30101085 1.21707466
[37] 1.13313848 1.04920230 0.96526611 0.88132993 0.79739375 0.71345756
[43] 0.62952138 0.54558519 0.46164901 0.37771283 0.29377664 0.20984046
[49] 0.12590428 0.04196809 0.04196809 0.12590428 0.20984046 0.29377664
[55] 0.37771283 0.46164901 0.54558519 0.62952138 0.71345756 0.79739375
[61] 0.88132993 0.96526611 1.04920230 1.13313848 1.21707466 1.30101085
[67] 1.38494703 1.46888322 1.55281940 1.63675558 1.72069177 1.80462795
[73] 1.88856413 1.97250032 2.05643650 2.14037269 2.22430887 2.30824505
[79] 2.39218124 2.47611742 2.56005360 2.64398979 2.72792597 2.81186216
[85] 2.89579834 2.97973452 3.06367071 3.14760689 3.23154307 3.31547926
[91] 3.39941544 3.48335163 3.56728781 3.65122399 3.73516018 3.81909636
[97] 3.90303254 3.98696873 4.07090491 4.15484109
[[5]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[5]][[1]]$xlab
[1] "YEAR"
[[5]][[1]]$ylab
[1] "s(YEAR,1)"
[[5]][[1]]$main
NULL
[[5]][[1]]$se.mult
[1] 2
[[5]][[1]]$xlim
[1] 1978 2007
[[5]][[1]]$fit
[,1]
[1,] -3.96129032
[2,] -3.88126426
[3,] -3.80123819
[4,] -3.72121212
[5,] -3.64118605
[6,] -3.56115999
[7,] -3.48113392
[8,] -3.40110785
[9,] -3.32108179
[10,] -3.24105572
[11,] -3.16102965
[12,] -3.08100358
[13,] -3.00097752
[14,] -2.92095145
[15,] -2.84092538
[16,] -2.76089932
[17,] -2.68087325
[18,] -2.60084718
[19,] -2.52082111
[20,] -2.44079505
[21,] -2.36076898
[22,] -2.28074291
[23,] -2.20071685
[24,] -2.12069078
[25,] -2.04066471
[26,] -1.96063864
[27,] -1.88061258
[28,] -1.80058651
[29,] -1.72056044
[30,] -1.64053438
[31,] -1.56050831
[32,] -1.48048224
[33,] -1.40045617
[34,] -1.32043011
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[39,] -0.92029977
[40,] -0.84027370
[41,] -0.76024764
[42,] -0.68022157
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[61,] 0.84027370
[62,] 0.92029977
[63,] 1.00032584
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[76,] 2.04066471
[77,] 2.12069078
[78,] 2.20071685
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[80,] 2.36076898
[81,] 2.44079505
[82,] 2.52082111
[83,] 2.60084718
[84,] 2.68087325
[85,] 2.76089932
[86,] 2.84092538
[87,] 2.92095145
[88,] 3.00097752
[89,] 3.08100358
[90,] 3.16102965
[91,] 3.24105572
[92,] 3.32108179
[93,] 3.40110785
[94,] 3.48113392
[95,] 3.56115999
[96,] 3.64118605
[97,] 3.72121212
[98,] 3.80123819
[99,] 3.88126426
[100,] 3.96129032
[[5]][[1]]$plot.me
[1] TRUE
[[6]]
[[6]][[1]]
[[6]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[6]][[1]]$scale
[1] TRUE
[[6]][[1]]$se
[1] 4.5749248 4.4822190 4.3895250 4.2968438 4.2041763 4.1115235 4.0188866
[8] 3.9262666 3.8336644 3.7410812 3.6485177 3.5559750 3.4634538 3.3709549
[15] 3.2784789 3.1860263 3.0935977 3.0011934 2.9088137 2.8164588 2.7241289
[22] 2.6318241 2.5395446 2.4472903 2.3550615 2.2628583 2.1706810 2.0785301
[29] 1.9864063 1.8943106 1.8022444 1.7102096 1.6182088 1.5262455 1.4343246
[36] 1.3424521 1.2506368 1.1588900 1.0672277 0.9756718 0.8842541 0.7930208
[43] 0.7020426 0.6114326 0.5213817 0.4322389 0.3447087 0.2604218 0.1838927
[50] 0.1296727 0.1296727 0.1838927 0.2604218 0.3447087 0.4322389 0.5213817
[57] 0.6114326 0.7020426 0.7930208 0.8842541 0.9756718 1.0672277 1.1588900
[64] 1.2506368 1.3424521 1.4343246 1.5262455 1.6182088 1.7102096 1.8022444
[71] 1.8943106 1.9864063 2.0785301 2.1706810 2.2628583 2.3550615 2.4472903
[78] 2.5395446 2.6318241 2.7241289 2.8164588 2.9088137 3.0011934 3.0935977
[85] 3.1860263 3.2784789 3.3709549 3.4634538 3.5559750 3.6485177 3.7410812
[92] 3.8336644 3.9262666 4.0188866 4.1115235 4.2041763 4.2968438 4.3895250
[99] 4.4822190 4.5749248
[[6]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[6]][[1]]$xlab
[1] "YEAR"
[[6]][[1]]$ylab
[1] "s(YEAR,1)"
[[6]][[1]]$main
NULL
[[6]][[1]]$se.mult
[1] 2
[[6]][[1]]$xlim
[1] 1978 2007
[[6]][[1]]$fit
[,1]
[1,] -3.35532657
[2,] -3.28743071
[3,] -3.21953493
[4,] -3.15163932
[5,] -3.08374394
[6,] -3.01584892
[7,] -2.94795439
[8,] -2.88006049
[9,] -2.81216737
[10,] -2.74427520
[11,] -2.67638416
[12,] -2.60849442
[13,] -2.54060617
[14,] -2.47271961
[15,] -2.40483495
[16,] -2.33695237
[17,] -2.26907209
[18,] -2.20119431
[19,] -2.13331924
[20,] -2.06544709
[21,] -1.99757805
[22,] -1.92971233
[23,] -1.86185014
[24,] -1.79399166
[25,] -1.72613709
[26,] -1.65828662
[27,] -1.59044043
[28,] -1.52259870
[29,] -1.45476159
[30,] -1.38692928
[31,] -1.31910192
[32,] -1.25127967
[33,] -1.18346267
[34,] -1.11565105
[35,] -1.04784494
[36,] -0.98004447
[37,] -0.91224975
[38,] -0.84446089
[39,] -0.77667797
[40,] -0.70890110
[41,] -0.64113035
[42,] -0.57336579
[43,] -0.50560748
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[57,] 0.44233732
[58,] 0.51000008
[59,] 0.57765674
[60,] 0.64530736
[61,] 0.71295204
[62,] 0.78059088
[63,] 0.84822396
[64,] 0.91585139
[65,] 0.98347330
[66,] 1.05108979
[67,] 1.11870100
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[70,] 1.32150428
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[72,] 1.45668263
[73,] 1.52426513
[74,] 1.59184338
[75,] 1.65941757
[76,] 1.72698786
[77,] 1.79455443
[78,] 1.86211746
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[80,] 1.99723365
[81,] 2.06478717
[82,] 2.13233790
[83,] 2.19988601
[84,] 2.26743172
[85,] 2.33497519
[86,] 2.40251662
[87,] 2.47005619
[88,] 2.53759409
[89,] 2.60513049
[90,] 2.67266557
[91,] 2.74019950
[92,] 2.80773244
[93,] 2.87526454
[94,] 2.94279596
[95,] 3.01032682
[96,] 3.07785725
[97,] 3.14538737
[98,] 3.21291728
[99,] 3.28044704
[100,] 3.34797674
[[6]][[1]]$plot.me
[1] TRUE
[[7]]
[[7]][[1]]
[[7]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[7]][[1]]$scale
[1] TRUE
[[7]][[1]]$se
[1] 4.113374 3.986321 3.860740 3.736810 3.614718 3.494672 3.376893 3.261609
[9] 3.149050 3.039450 2.933043 2.830051 2.730688 2.635155 2.543629 2.456267
[17] 2.373195 2.294509 2.220267 2.150490 2.085159 2.024212 1.967547 1.915027
[25] 1.866475 1.821682 1.780423 1.742449 1.707497 1.675306 1.645624 1.618199
[33] 1.592799 1.569224 1.547294 1.526848 1.507772 1.489980 1.473406 1.458018
[41] 1.443818 1.430820 1.419055 1.408575 1.399440 1.391705 1.385431 1.380675
[49] 1.377478 1.375870 1.375870 1.377478 1.380675 1.385431 1.391705 1.399440
[57] 1.408575 1.419055 1.430820 1.443818 1.458018 1.473406 1.489980 1.507772
[65] 1.526848 1.547294 1.569224 1.592799 1.618199 1.645624 1.675306 1.707497
[73] 1.742449 1.780423 1.821682 1.866475 1.915027 1.967547 2.024212 2.085159
[81] 2.150490 2.220267 2.294509 2.373195 2.456267 2.543629 2.635155 2.730688
[89] 2.830051 2.933043 3.039450 3.149050 3.261609 3.376893 3.494672 3.614718
[97] 3.736810 3.860740 3.986321 4.113374
[[7]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[7]][[1]]$xlab
[1] "YEAR"
[[7]][[1]]$ylab
[1] "s(YEAR,1.37)"
[[7]][[1]]$main
NULL
[[7]][[1]]$se.mult
[1] 2
[[7]][[1]]$xlim
[1] 1978 2007
[[7]][[1]]$fit
[,1]
[1,] -4.72624125
[2,] -4.60219429
[3,] -4.47817642
[4,] -4.35421673
[5,] -4.23034499
[6,] -4.10660161
[7,] -3.98303553
[8,] -3.85969592
[9,] -3.73663516
[10,] -3.61391338
[11,] -3.49159185
[12,] -3.36973221
[13,] -3.24839929
[14,] -3.12765951
[15,] -3.00757931
[16,] -2.88822487
[17,] -2.76966197
[18,] -2.65195634
[19,] -2.53517300
[20,] -2.41937331
[21,] -2.30461752
[22,] -2.19096568
[23,] -2.07847331
[24,] -1.96719161
[25,] -1.85717161
[26,] -1.74846171
[27,] -1.64110247
[28,] -1.53513308
[29,] -1.43059193
[30,] -1.32750956
[31,] -1.22591169
[32,] -1.12582392
[33,] -1.02726716
[34,] -0.93025380
[35,] -0.83479533
[36,] -0.74090177
[37,] -0.64857409
[38,] -0.55780985
[39,] -0.46860643
[40,] -0.38095544
[41,] -0.29484187
[42,] -0.21025037
[43,] -0.12716350
[44,] -0.04555630
[45,] 0.03459787
[46,] 0.11332601
[47,] 0.19066018
[48,] 0.26663607
[49,] 0.34128950
[50,] 0.41465820
[51,] 0.48678411
[52,] 0.55770973
[53,] 0.62747790
[54,] 0.69613403
[55,] 0.76372474
[56,] 0.83029662
[57,] 0.89589691
[58,] 0.96057367
[59,] 1.02437503
[60,] 1.08734897
[61,] 1.14954290
[62,] 1.21100406
[63,] 1.27177959
[64,] 1.33191513
[65,] 1.39145497
[66,] 1.45044337
[67,] 1.50892343
[68,] 1.56693525
[69,] 1.62451841
[70,] 1.68171213
[71,] 1.73855212
[72,] 1.79507213
[73,] 1.85130588
[74,] 1.90728477
[75,] 1.96303640
[76,] 2.01858802
[77,] 2.07396608
[78,] 2.12919270
[79,] 2.18428851
[80,] 2.23927404
[81,] 2.29416689
[82,] 2.34898163
[83,] 2.40373265
[84,] 2.45843326
[85,] 2.51309319
[86,] 2.56772142
[87,] 2.62232672
[88,] 2.67691543
[89,] 2.73149225
[90,] 2.78606183
[91,] 2.84062791
[92,] 2.89519234
[93,] 2.94975679
[94,] 3.00432272
[95,] 3.05889055
[96,] 3.11346022
[97,] 3.16803169
[98,] 3.22260469
[99,] 3.27717874
[100,] 3.33175330
[[7]][[1]]$plot.me
[1] TRUE
[[8]]
[[8]][[1]]
[[8]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[8]][[1]]$scale
[1] TRUE
[[8]][[1]]$se
[1] 5.42431599 5.31473385 5.20515171 5.09556957 4.98598743 4.87640529
[7] 4.76682315 4.65724101 4.54765886 4.43807672 4.32849458 4.21891244
[13] 4.10933030 3.99974816 3.89016602 3.78058387 3.67100173 3.56141959
[19] 3.45183745 3.34225531 3.23267317 3.12309103 3.01350889 2.90392674
[25] 2.79434460 2.68476246 2.57518032 2.46559818 2.35601604 2.24643390
[31] 2.13685176 2.02726961 1.91768747 1.80810533 1.69852319 1.58894105
[37] 1.47935891 1.36977677 1.26019463 1.15061248 1.04103034 0.93144820
[43] 0.82186606 0.71228392 0.60270178 0.49311964 0.38353750 0.27395535
[49] 0.16437321 0.05479108 0.05479108 0.16437321 0.27395535 0.38353750
[55] 0.49311964 0.60270178 0.71228392 0.82186606 0.93144820 1.04103034
[61] 1.15061248 1.26019463 1.36977677 1.47935891 1.58894105 1.69852319
[67] 1.80810533 1.91768747 2.02726961 2.13685176 2.24643390 2.35601604
[73] 2.46559818 2.57518032 2.68476246 2.79434460 2.90392674 3.01350889
[79] 3.12309103 3.23267317 3.34225531 3.45183745 3.56141959 3.67100173
[85] 3.78058387 3.89016602 3.99974816 4.10933030 4.21891244 4.32849458
[91] 4.43807672 4.54765886 4.65724101 4.76682315 4.87640529 4.98598743
[97] 5.09556957 5.20515171 5.31473385 5.42431599
[[8]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[8]][[1]]$xlab
[1] "YEAR"
[[8]][[1]]$ylab
[1] "s(YEAR,1)"
[[8]][[1]]$main
NULL
[[8]][[1]]$se.mult
[1] 2
[[8]][[1]]$xlim
[1] 1978 2007
[[8]][[1]]$fit
[,1]
[1,] -3.11612903
[2,] -3.05317693
[3,] -2.99022483
[4,] -2.92727273
[5,] -2.86432063
[6,] -2.80136852
[7,] -2.73841642
[8,] -2.67546432
[9,] -2.61251222
[10,] -2.54956012
[11,] -2.48660802
[12,] -2.42365591
[13,] -2.36070381
[14,] -2.29775171
[15,] -2.23479961
[16,] -2.17184751
[17,] -2.10889541
[18,] -2.04594330
[19,] -1.98299120
[20,] -1.92003910
[21,] -1.85708700
[22,] -1.79413490
[23,] -1.73118280
[24,] -1.66823069
[25,] -1.60527859
[26,] -1.54232649
[27,] -1.47937439
[28,] -1.41642229
[29,] -1.35347019
[30,] -1.29051808
[31,] -1.22756598
[32,] -1.16461388
[33,] -1.10166178
[34,] -1.03870968
[35,] -0.97575758
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[75,] 1.54232649
[76,] 1.60527859
[77,] 1.66823069
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[82,] 1.98299120
[83,] 2.04594330
[84,] 2.10889541
[85,] 2.17184751
[86,] 2.23479961
[87,] 2.29775171
[88,] 2.36070381
[89,] 2.42365591
[90,] 2.48660802
[91,] 2.54956012
[92,] 2.61251222
[93,] 2.67546432
[94,] 2.73841642
[95,] 2.80136852
[96,] 2.86432063
[97,] 2.92727273
[98,] 2.99022483
[99,] 3.05317693
[100,] 3.11612903
[[8]][[1]]$plot.me
[1] TRUE
[[9]]
[[9]][[1]]
[[9]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[9]][[1]]$scale
[1] TRUE
[[9]][[1]]$se
[1] 4.3272802 4.2398604 4.1524406 4.0650208 3.9776010 3.8901812 3.8027613
[8] 3.7153415 3.6279217 3.5405019 3.4530821 3.3656623 3.2782425 3.1908227
[15] 3.1034029 3.0159831 2.9285633 2.8411435 2.7537237 2.6663039 2.5788841
[22] 2.4914643 2.4040445 2.3166247 2.2292049 2.1417851 2.0543653 1.9669455
[29] 1.8795257 1.7921059 1.7046861 1.6172663 1.5298465 1.4424267 1.3550069
[36] 1.2675871 1.1801673 1.0927475 1.0053277 0.9179079 0.8304881 0.7430683
[43] 0.6556485 0.5682287 0.4808089 0.3933891 0.3059693 0.2185495 0.1311297
[50] 0.0437099 0.0437099 0.1311297 0.2185495 0.3059693 0.3933891 0.4808089
[57] 0.5682287 0.6556485 0.7430683 0.8304881 0.9179079 1.0053277 1.0927475
[64] 1.1801673 1.2675871 1.3550069 1.4424267 1.5298465 1.6172663 1.7046861
[71] 1.7921059 1.8795257 1.9669455 2.0543653 2.1417851 2.2292049 2.3166247
[78] 2.4040445 2.4914643 2.5788841 2.6663039 2.7537237 2.8411435 2.9285633
[85] 3.0159831 3.1034029 3.1908227 3.2782425 3.3656623 3.4530821 3.5405019
[92] 3.6279217 3.7153415 3.8027613 3.8901812 3.9776010 4.0650208 4.1524406
[99] 4.2398604 4.3272802
[[9]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[9]][[1]]$xlab
[1] "YEAR"
[[9]][[1]]$ylab
[1] "s(YEAR,1)"
[[9]][[1]]$main
NULL
[[9]][[1]]$se.mult
[1] 2
[[9]][[1]]$xlim
[1] 1978 2007
[[9]][[1]]$fit
[,1]
[1,] 7.48064516
[2,] 7.32952102
[3,] 7.17839687
[4,] 7.02727273
[5,] 6.87614858
[6,] 6.72502444
[7,] 6.57390029
[8,] 6.42277615
[9,] 6.27165200
[10,] 6.12052786
[11,] 5.96940371
[12,] 5.81827957
[13,] 5.66715543
[14,] 5.51603128
[15,] 5.36490714
[16,] 5.21378299
[17,] 5.06265885
[18,] 4.91153470
[19,] 4.76041056
[20,] 4.60928641
[21,] 4.45816227
[22,] 4.30703812
[23,] 4.15591398
[24,] 4.00478983
[25,] 3.85366569
[26,] 3.70254154
[27,] 3.55141740
[28,] 3.40029326
[29,] 3.24916911
[30,] 3.09804497
[31,] 2.94692082
[32,] 2.79579668
[33,] 2.64467253
[34,] 2.49354839
[35,] 2.34242424
[36,] 2.19130010
[37,] 2.04017595
[38,] 1.88905181
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[40,] 1.58680352
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[44,] 0.98230694
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[98,] -7.17839687
[99,] -7.32952102
[100,] -7.48064516
[[9]][[1]]$plot.me
[1] TRUE
[[10]]
[[10]][[1]]
[[10]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[10]][[1]]$scale
[1] TRUE
[[10]][[1]]$se
[1] 2.75292926 2.69731452 2.64169979 2.58608506 2.53047033 2.47485559
[7] 2.41924086 2.36362613 2.30801140 2.25239666 2.19678193 2.14116720
[13] 2.08555247 2.02993773 1.97432300 1.91870827 1.86309354 1.80747881
[19] 1.75186407 1.69624934 1.64063461 1.58501988 1.52940514 1.47379041
[25] 1.41817568 1.36256095 1.30694621 1.25133148 1.19571675 1.14010202
[31] 1.08448728 1.02887255 0.97325782 0.91764309 0.86202835 0.80641362
[37] 0.75079889 0.69518416 0.63956942 0.58395469 0.52833996 0.47272523
[43] 0.41711049 0.36149576 0.30588103 0.25026630 0.19465156 0.13903683
[49] 0.08342210 0.02780737 0.02780737 0.08342210 0.13903683 0.19465156
[55] 0.25026630 0.30588103 0.36149576 0.41711049 0.47272523 0.52833996
[61] 0.58395469 0.63956942 0.69518416 0.75079889 0.80641362 0.86202835
[67] 0.91764309 0.97325782 1.02887255 1.08448728 1.14010202 1.19571675
[73] 1.25133148 1.30694621 1.36256095 1.41817568 1.47379041 1.52940514
[79] 1.58501988 1.64063461 1.69624934 1.75186407 1.80747881 1.86309354
[85] 1.91870827 1.97432300 2.02993773 2.08555247 2.14116720 2.19678193
[91] 2.25239666 2.30801140 2.36362613 2.41924086 2.47485559 2.53047033
[97] 2.58608506 2.64169979 2.69731452 2.75292926
[[10]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[10]][[1]]$xlab
[1] "YEAR"
[[10]][[1]]$ylab
[1] "s(YEAR,1)"
[[10]][[1]]$main
NULL
[[10]][[1]]$se.mult
[1] 2
[[10]][[1]]$xlim
[1] 1978 2007
[[10]][[1]]$fit
[,1]
[1,] -2.39032258
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[3,] -2.29374389
[4,] -2.24545455
[5,] -2.19716520
[6,] -2.14887586
[7,] -2.10058651
[8,] -2.05229717
[9,] -2.00400782
[10,] -1.95571848
[11,] -1.90742913
[12,] -1.85913978
[13,] -1.81085044
[14,] -1.76256109
[15,] -1.71427175
[16,] -1.66598240
[17,] -1.61769306
[18,] -1.56940371
[19,] -1.52111437
[20,] -1.47282502
[21,] -1.42453568
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[24,] -1.27966764
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[27,] -1.13479961
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[33,] -0.84506354
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[77,] 1.27966764
[78,] 1.32795699
[79,] 1.37624633
[80,] 1.42453568
[81,] 1.47282502
[82,] 1.52111437
[83,] 1.56940371
[84,] 1.61769306
[85,] 1.66598240
[86,] 1.71427175
[87,] 1.76256109
[88,] 1.81085044
[89,] 1.85913978
[90,] 1.90742913
[91,] 1.95571848
[92,] 2.00400782
[93,] 2.05229717
[94,] 2.10058651
[95,] 2.14887586
[96,] 2.19716520
[97,] 2.24545455
[98,] 2.29374389
[99,] 2.34203324
[100,] 2.39032258
[[10]][[1]]$plot.me
[1] TRUE
[[11]]
[[11]][[1]]
[[11]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[11]][[1]]$scale
[1] TRUE
[[11]][[1]]$se
[1] 3.06815016 3.00616733 2.94418450 2.88220167 2.82021884 2.75823600
[7] 2.69625317 2.63427034 2.57228751 2.51030468 2.44832185 2.38633901
[13] 2.32435618 2.26237335 2.20039052 2.13840769 2.07642486 2.01444203
[19] 1.95245919 1.89047636 1.82849353 1.76651070 1.70452787 1.64254504
[25] 1.58056220 1.51857937 1.45659654 1.39461371 1.33263088 1.27064805
[31] 1.20866522 1.14668238 1.08469955 1.02271672 0.96073389 0.89875106
[37] 0.83676823 0.77478539 0.71280256 0.65081973 0.58883690 0.52685407
[43] 0.46487124 0.40288841 0.34090557 0.27892274 0.21693991 0.15495708
[49] 0.09297425 0.03099142 0.03099142 0.09297425 0.15495708 0.21693991
[55] 0.27892274 0.34090557 0.40288841 0.46487124 0.52685407 0.58883690
[61] 0.65081973 0.71280256 0.77478539 0.83676823 0.89875106 0.96073389
[67] 1.02271672 1.08469955 1.14668238 1.20866522 1.27064805 1.33263088
[73] 1.39461371 1.45659654 1.51857937 1.58056220 1.64254504 1.70452787
[79] 1.76651070 1.82849353 1.89047636 1.95245919 2.01444203 2.07642486
[85] 2.13840769 2.20039052 2.26237335 2.32435618 2.38633901 2.44832185
[91] 2.51030468 2.57228751 2.63427034 2.69625317 2.75823600 2.82021884
[97] 2.88220167 2.94418450 3.00616733 3.06815016
[[11]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[11]][[1]]$xlab
[1] "YEAR"
[[11]][[1]]$ylab
[1] "s(YEAR,1)"
[[11]][[1]]$main
NULL
[[11]][[1]]$se.mult
[1] 2
[[11]][[1]]$xlim
[1] 1978 2007
[[11]][[1]]$fit
[,1]
[1,] -5.77419355
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[4,] -5.42424242
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[7,] -5.07429130
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[9,] -4.84099055
[10,] -4.72434018
[11,] -4.60768980
[12,] -4.49103943
[13,] -4.37438905
[14,] -4.25773868
[15,] -4.14108830
[16,] -4.02443793
[17,] -3.90778755
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[29,] -2.50798306
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[33,] -2.04138156
[34,] -1.92473118
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[60,] 1.10817856
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[78,] 3.20788530
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[81,] 3.55783643
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[83,] 3.79113718
[84,] 3.90778755
[85,] 4.02443793
[86,] 4.14108830
[87,] 4.25773868
[88,] 4.37438905
[89,] 4.49103943
[90,] 4.60768980
[91,] 4.72434018
[92,] 4.84099055
[93,] 4.95764093
[94,] 5.07429130
[95,] 5.19094167
[96,] 5.30759205
[97,] 5.42424242
[98,] 5.54089280
[99,] 5.65754317
[100,] 5.77419355
[[11]][[1]]$plot.me
[1] TRUE
[[12]]
[[12]][[1]]
[[12]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[12]][[1]]$scale
[1] TRUE
[[12]][[1]]$se
[1] 4.555740 4.339754 4.127369 3.919273 3.716234 3.519151 3.329047 3.147022
[9] 2.974268 2.812064 2.661725 2.524553 2.401785 2.294495 2.203490 2.129204
[17] 2.071607 2.030139 2.003708 1.990773 1.989435 1.997560 2.012957 2.033502
[25] 2.057185 2.082185 2.106963 2.130201 2.150788 2.167884 2.180874 2.189296
[33] 2.192878 2.191560 2.185404 2.174587 2.159467 2.140517 2.118285 2.093440
[41] 2.066760 2.039069 2.011237 1.984192 1.958856 1.936109 1.916777 1.901588
[49] 1.891120 1.885778 1.885778 1.891120 1.901588 1.916777 1.936109 1.958856
[57] 1.984192 2.011237 2.039069 2.066760 2.093440 2.118285 2.140517 2.159467
[65] 2.174587 2.185404 2.191560 2.192878 2.189296 2.180874 2.167884 2.150788
[73] 2.130201 2.106963 2.082185 2.057185 2.033502 2.012957 1.997560 1.989435
[81] 1.990773 2.003708 2.030139 2.071607 2.129204 2.203490 2.294495 2.401785
[89] 2.524553 2.661725 2.812064 2.974268 3.147022 3.329047 3.519151 3.716234
[97] 3.919273 4.127369 4.339754 4.555740
[[12]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[12]][[1]]$xlab
[1] "YEAR"
[[12]][[1]]$ylab
[1] "s(YEAR,2.47)"
[[12]][[1]]$main
NULL
[[12]][[1]]$se.mult
[1] 2
[[12]][[1]]$xlim
[1] 1978 2007
[[12]][[1]]$fit
[,1]
[1,] -2.36830005
[2,] -2.15101870
[3,] -1.93396467
[4,] -1.71736526
[5,] -1.50145295
[6,] -1.28654169
[7,] -1.07301049
[8,] -0.86124024
[9,] -0.65163486
[10,] -0.44465376
[11,] -0.24076457
[12,] -0.04043695
[13,] 0.15584237
[14,] 0.34757806
[15,] 0.53427486
[16,] 0.71544620
[17,] 0.89061852
[18,] 1.05931934
[19,] 1.22108486
[20,] 1.37549402
[21,] 1.52213894
[22,] 1.66061392
[23,] 1.79056063
[24,] 1.91166600
[25,] 2.02361879
[26,] 2.12613426
[27,] 2.21900567
[28,] 2.30204052
[29,] 2.37505350
[30,] 2.43793589
[31,] 2.49062548
[32,] 2.53306115
[33,] 2.56522612
[34,] 2.58718374
[35,] 2.59900580
[36,] 2.60077764
[37,] 2.59266689
[38,] 2.57487207
[39,] 2.54759346
[40,] 2.51108138
[41,] 2.46564349
[42,] 2.41159057
[43,] 2.34925017
[44,] 2.27901040
[45,] 2.20127298
[46,] 2.11644223
[47,] 2.02495804
[48,] 1.92728624
[49,] 1.82389329
[50,] 1.71525578
[51,] 1.60187242
[52,] 1.48424486
[53,] 1.36287512
[54,] 1.23826806
[55,] 1.11092987
[56,] 0.98136650
[57,] 0.85007371
[58,] 0.71753329
[59,] 0.58422603
[60,] 0.45062480
[61,] 0.31716742
[62,] 0.18428195
[63,] 0.05239439
[64,] -0.07810794
[65,] -0.20687142
[66,] -0.33354361
[67,] -0.45779470
[68,] -0.57935501
[69,] -0.69796473
[70,] -0.81337061
[71,] -0.92538114
[72,] -1.03383895
[73,] -1.13858757
[74,] -1.23950783
[75,] -1.33654211
[76,] -1.42963855
[77,] -1.51875720
[78,] -1.60392337
[79,] -1.68518458
[80,] -1.76258994
[81,] -1.83622869
[82,] -1.90623202
[83,] -1.97273309
[84,] -2.03587817
[85,] -2.09585608
[86,] -2.15286432
[87,] -2.20710208
[88,] -2.25878916
[89,] -2.30815902
[90,] -2.35544542
[91,] -2.40088281
[92,] -2.44470715
[93,] -2.48715456
[94,] -2.52845775
[95,] -2.56882639
[96,] -2.60846059
[97,] -2.64755949
[98,] -2.68628925
[99,] -2.72477466
[100,] -2.76313789
[[12]][[1]]$plot.me
[1] TRUE
[[13]]
[[13]][[1]]
[[13]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[13]][[1]]$scale
[1] TRUE
[[13]][[1]]$se
[1] 2.800206 2.706481 2.613945 2.522754 2.433074 2.345089 2.259002 2.175018
[9] 2.093349 2.014213 1.937828 1.864404 1.794146 1.727243 1.663867 1.604163
[17] 1.548249 1.496209 1.448083 1.403872 1.363531 1.326964 1.294032 1.264558
[25] 1.238322 1.215072 1.194539 1.176442 1.160486 1.146388 1.133879 1.122704
[33] 1.112629 1.103461 1.095029 1.087189 1.079841 1.072912 1.066352 1.060141
[41] 1.054286 1.048809 1.043743 1.039140 1.035056 1.031542 1.028655 1.026443
[49] 1.024947 1.024190 1.024190 1.024947 1.026443 1.028655 1.031542 1.035056
[57] 1.039140 1.043743 1.048809 1.054286 1.060141 1.066352 1.072912 1.079841
[65] 1.087189 1.095029 1.103461 1.112629 1.122704 1.133879 1.146388 1.160486
[73] 1.176442 1.194539 1.215072 1.238322 1.264558 1.294032 1.326964 1.363531
[81] 1.403872 1.448083 1.496209 1.548249 1.604163 1.663867 1.727243 1.794146
[89] 1.864404 1.937828 2.014213 2.093349 2.175018 2.259002 2.345089 2.433074
[97] 2.522754 2.613945 2.706481 2.800206
[[13]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[13]][[1]]$xlab
[1] "YEAR"
[[13]][[1]]$ylab
[1] "s(YEAR,1.5)"
[[13]][[1]]$main
NULL
[[13]][[1]]$se.mult
[1] 2
[[13]][[1]]$xlim
[1] 1978 2007
[[13]][[1]]$fit
[,1]
[1,] -0.060627161
[2,] -0.032902095
[3,] -0.005201845
[4,] 0.022448773
[5,] 0.050024365
[6,] 0.077490374
[7,] 0.104804928
[8,] 0.131925944
[9,] 0.158808521
[10,] 0.185400957
[11,] 0.211650548
[12,] 0.237504230
[13,] 0.262905917
[14,] 0.287798000
[15,] 0.312122858
[16,] 0.335822833
[17,] 0.358840212
[18,] 0.381117276
[19,] 0.402596822
[20,] 0.423224181
[21,] 0.442945464
[22,] 0.461706940
[23,] 0.479458254
[24,] 0.496152273
[25,] 0.511741997
[26,] 0.526182456
[27,] 0.539434655
[28,] 0.551460695
[29,] 0.562223246
[30,] 0.571691137
[31,] 0.579836926
[32,] 0.586633263
[33,] 0.592056512
[34,] 0.596089756
[35,] 0.598716785
[36,] 0.599922581
[37,] 0.599699380
[38,] 0.598042140
[39,] 0.594945982
[40,] 0.590410752
[41,] 0.584441700
[42,] 0.577044374
[43,] 0.568226075
[44,] 0.558000439
[45,] 0.546382526
[46,] 0.533387721
[47,] 0.519035851
[48,] 0.503349985
[49,] 0.486353272
[50,] 0.468070699
[51,] 0.448531274
[52,] 0.427764535
[53,] 0.405800403
[54,] 0.382671681
[55,] 0.358412493
[56,] 0.333056992
[57,] 0.306640447
[58,] 0.279199651
[59,] 0.250771508
[60,] 0.221393080
[61,] 0.191102133
[62,] 0.159936628
[63,] 0.127934511
[64,] 0.095133487
[65,] 0.061571048
[66,] 0.027284679
[67,] -0.007688564
[68,] -0.043312758
[69,] -0.079552168
[70,] -0.116371234
[71,] -0.153736031
[72,] -0.191613542
[73,] -0.229970775
[74,] -0.268775941
[75,] -0.307999233
[76,] -0.347611030
[77,] -0.387582160
[78,] -0.427885909
[79,] -0.468496402
[80,] -0.509387834
[81,] -0.550536204
[82,] -0.591919394
[83,] -0.633515375
[84,] -0.675302883
[85,] -0.717263145
[86,] -0.759377893
[87,] -0.801629027
[88,] -0.844000483
[89,] -0.886477551
[90,] -0.929045552
[91,] -0.971690867
[92,] -1.014401981
[93,] -1.057167629
[94,] -1.099976866
[95,] -1.142820918
[96,] -1.185691915
[97,] -1.228582030
[98,] -1.271484976
[99,] -1.314396395
[100,] -1.357312050
[[13]][[1]]$plot.me
[1] TRUE
[[14]]
[[14]][[1]]
[[14]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[14]][[1]]$scale
[1] TRUE
[[14]][[1]]$se
[1] 3.7393685 3.6638257 3.5882829 3.5127401 3.4371973 3.3616545 3.2861117
[8] 3.2105689 3.1350261 3.0594833 2.9839405 2.9083977 2.8328549 2.7573121
[15] 2.6817693 2.6062265 2.5306837 2.4551410 2.3795982 2.3040554 2.2285126
[22] 2.1529698 2.0774270 2.0018842 1.9263414 1.8507986 1.7752558 1.6997130
[29] 1.6241702 1.5486274 1.4730846 1.3975418 1.3219990 1.2464562 1.1709134
[36] 1.0953706 1.0198278 0.9442850 0.8687422 0.7931994 0.7176566 0.6421138
[43] 0.5665710 0.4910282 0.4154854 0.3399426 0.2643998 0.1888570 0.1133142
[50] 0.0377714 0.0377714 0.1133142 0.1888570 0.2643998 0.3399426 0.4154854
[57] 0.4910282 0.5665710 0.6421138 0.7176566 0.7931994 0.8687422 0.9442850
[64] 1.0198278 1.0953706 1.1709134 1.2464562 1.3219990 1.3975418 1.4730846
[71] 1.5486274 1.6241702 1.6997130 1.7752558 1.8507986 1.9263414 2.0018842
[78] 2.0774270 2.1529698 2.2285126 2.3040554 2.3795982 2.4551410 2.5306837
[85] 2.6062265 2.6817693 2.7573121 2.8328549 2.9083977 2.9839405 3.0594833
[92] 3.1350261 3.2105689 3.2861117 3.3616545 3.4371973 3.5127401 3.5882829
[99] 3.6638257 3.7393685
[[14]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[14]][[1]]$xlab
[1] "YEAR"
[[14]][[1]]$ylab
[1] "s(YEAR,1)"
[[14]][[1]]$main
NULL
[[14]][[1]]$se.mult
[1] 2
[[14]][[1]]$xlim
[1] 1978 2007
[[14]][[1]]$fit
[,1]
[1,] 6.63548387
[2,] 6.50143369
[3,] 6.36738351
[4,] 6.23333333
[5,] 6.09928315
[6,] 5.96523297
[7,] 5.83118280
[8,] 5.69713262
[9,] 5.56308244
[10,] 5.42903226
[11,] 5.29498208
[12,] 5.16093190
[13,] 5.02688172
[14,] 4.89283154
[15,] 4.75878136
[16,] 4.62473118
[17,] 4.49068100
[18,] 4.35663082
[19,] 4.22258065
[20,] 4.08853047
[21,] 3.95448029
[22,] 3.82043011
[23,] 3.68637993
[24,] 3.55232975
[25,] 3.41827957
[26,] 3.28422939
[27,] 3.15017921
[28,] 3.01612903
[29,] 2.88207885
[30,] 2.74802867
[31,] 2.61397849
[32,] 2.47992832
[33,] 2.34587814
[34,] 2.21182796
[35,] 2.07777778
[36,] 1.94372760
[37,] 1.80967742
[38,] 1.67562724
[39,] 1.54157706
[40,] 1.40752688
[41,] 1.27347670
[42,] 1.13942652
[43,] 1.00537634
[44,] 0.87132616
[45,] 0.73727599
[46,] 0.60322581
[47,] 0.46917563
[48,] 0.33512545
[49,] 0.20107527
[50,] 0.06702509
[51,] -0.06702509
[52,] -0.20107527
[53,] -0.33512545
[54,] -0.46917563
[55,] -0.60322581
[56,] -0.73727599
[57,] -0.87132616
[58,] -1.00537634
[59,] -1.13942652
[60,] -1.27347670
[61,] -1.40752688
[62,] -1.54157706
[63,] -1.67562724
[64,] -1.80967742
[65,] -1.94372760
[66,] -2.07777778
[67,] -2.21182796
[68,] -2.34587814
[69,] -2.47992832
[70,] -2.61397849
[71,] -2.74802867
[72,] -2.88207885
[73,] -3.01612903
[74,] -3.15017921
[75,] -3.28422939
[76,] -3.41827957
[77,] -3.55232975
[78,] -3.68637993
[79,] -3.82043011
[80,] -3.95448029
[81,] -4.08853047
[82,] -4.22258065
[83,] -4.35663082
[84,] -4.49068100
[85,] -4.62473118
[86,] -4.75878136
[87,] -4.89283154
[88,] -5.02688172
[89,] -5.16093190
[90,] -5.29498208
[91,] -5.42903226
[92,] -5.56308244
[93,] -5.69713262
[94,] -5.83118280
[95,] -5.96523297
[96,] -6.09928315
[97,] -6.23333333
[98,] -6.36738351
[99,] -6.50143369
[100,] -6.63548387
[[14]][[1]]$plot.me
[1] TRUE
[[15]]
[[15]][[1]]
[[15]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[15]][[1]]$scale
[1] TRUE
[[15]][[1]]$se
[1] 9.9056269 9.7055133 9.5053996 9.3052859 9.1051722 8.9050586 8.7049449
[8] 8.5048312 8.3047175 8.1046039 7.9044902 7.7043765 7.5042628 7.3041492
[15] 7.1040355 6.9039218 6.7038081 6.5036945 6.3035808 6.1034671 5.9033534
[22] 5.7032397 5.5031261 5.3030124 5.1028987 4.9027850 4.7026714 4.5025577
[29] 4.3024440 4.1023303 3.9022167 3.7021030 3.5019893 3.3018756 3.1017620
[36] 2.9016483 2.7015346 2.5014209 2.3013073 2.1011936 1.9010799 1.7009662
[43] 1.5008526 1.3007389 1.1006252 0.9005115 0.7003979 0.5002842 0.3001705
[50] 0.1000568 0.1000568 0.3001705 0.5002842 0.7003979 0.9005115 1.1006252
[57] 1.3007389 1.5008526 1.7009662 1.9010799 2.1011936 2.3013073 2.5014209
[64] 2.7015346 2.9016483 3.1017620 3.3018756 3.5019893 3.7021030 3.9022167
[71] 4.1023303 4.3024440 4.5025577 4.7026714 4.9027850 5.1028987 5.3030124
[78] 5.5031261 5.7032397 5.9033534 6.1034671 6.3035808 6.5036945 6.7038081
[85] 6.9039218 7.1040355 7.3041492 7.5042628 7.7043765 7.9044902 8.1046039
[92] 8.3047175 8.5048312 8.7049449 8.9050586 9.1051722 9.3052859 9.5053996
[99] 9.7055133 9.9056269
[[15]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[15]][[1]]$xlab
[1] "YEAR"
[[15]][[1]]$ylab
[1] "s(YEAR,1)"
[[15]][[1]]$main
NULL
[[15]][[1]]$se.mult
[1] 2
[[15]][[1]]$xlim
[1] 1978 2007
[[15]][[1]]$fit
[,1]
[1,] -4.26129032
[2,] -4.17520365
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[95,] 3.83085696
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[100,] 4.26129032
[[15]][[1]]$plot.me
[1] TRUE
[[16]]
[[16]][[1]]
[[16]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[16]][[1]]$scale
[1] TRUE
[[16]][[1]]$se
[1] 6.746028 6.443908 6.146648 5.855122 5.570292 5.293278 5.025339 4.767815
[9] 4.522143 4.289853 4.072507 3.871652 3.688768 3.525179 3.381943 3.259754
[17] 3.158840 3.078878 3.018954 2.977613 2.952913 2.942530 2.943940 2.954572
[25] 2.971877 2.993455 3.017190 3.041205 3.063869 3.083894 3.100281 3.112245
[33] 3.119260 3.121084 3.117648 3.109043 3.095599 3.077797 3.056219 3.031593
[41] 3.004779 2.976687 2.948271 2.920547 2.894515 2.871109 2.851206 2.835568
[49] 2.824791 2.819291 2.819291 2.824791 2.835568 2.851206 2.871109 2.894515
[57] 2.920547 2.948271 2.976687 3.004779 3.031593 3.056219 3.077797 3.095599
[65] 3.109043 3.117648 3.121084 3.119260 3.112245 3.100281 3.083894 3.063869
[73] 3.041205 3.017190 2.993455 2.971877 2.954572 2.943940 2.942530 2.952913
[81] 2.977613 3.018954 3.078878 3.158840 3.259754 3.381943 3.525179 3.688768
[89] 3.871652 4.072507 4.289853 4.522143 4.767815 5.025339 5.293278 5.570292
[97] 5.855122 6.146648 6.443908 6.746028
[[16]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[16]][[1]]$xlab
[1] "YEAR"
[[16]][[1]]$ylab
[1] "s(YEAR,2.27)"
[[16]][[1]]$main
NULL
[[16]][[1]]$se.mult
[1] 2
[[16]][[1]]$xlim
[1] 1978 2007
[[16]][[1]]$fit
[,1]
[1,] -16.436496520
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[3,] -15.225307100
[4,] -14.620259285
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[6,] -13.412454098
[7,] -12.810374346
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[10,] -11.016073622
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[12,] -9.834339202
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[14,] -8.668760063
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[27,] -1.777262510
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[100,] -0.355112365
[[16]][[1]]$plot.me
[1] TRUE
[[17]]
[[17]][[1]]
[[17]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[17]][[1]]$scale
[1] TRUE
[[17]][[1]]$se
[1] 2.94883411 2.88926170 2.82968930 2.77011689 2.71054449 2.65097208
[7] 2.59139967 2.53182727 2.47225486 2.41268245 2.35311005 2.29353764
[13] 2.23396524 2.17439283 2.11482042 2.05524802 1.99567561 1.93610320
[19] 1.87653080 1.81695839 1.75738599 1.69781358 1.63824117 1.57866877
[25] 1.51909636 1.45952395 1.39995155 1.34037914 1.28080674 1.22123433
[31] 1.16166192 1.10208952 1.04251711 0.98294470 0.92337230 0.86379989
[37] 0.80422748 0.74465508 0.68508267 0.62551027 0.56593786 0.50636545
[43] 0.44679305 0.38722064 0.32764823 0.26807583 0.20850342 0.14893102
[49] 0.08935861 0.02978621 0.02978621 0.08935861 0.14893102 0.20850342
[55] 0.26807583 0.32764823 0.38722064 0.44679305 0.50636545 0.56593786
[61] 0.62551027 0.68508267 0.74465508 0.80422748 0.86379989 0.92337230
[67] 0.98294470 1.04251711 1.10208952 1.16166192 1.22123433 1.28080674
[73] 1.34037914 1.39995155 1.45952395 1.51909636 1.57866877 1.63824117
[79] 1.69781358 1.75738599 1.81695839 1.87653080 1.93610320 1.99567561
[85] 2.05524802 2.11482042 2.17439283 2.23396524 2.29353764 2.35311005
[91] 2.41268245 2.47225486 2.53182727 2.59139967 2.65097208 2.71054449
[97] 2.77011689 2.82968930 2.88926170 2.94883411
[[17]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[17]][[1]]$xlab
[1] "YEAR"
[[17]][[1]]$ylab
[1] "s(YEAR,1)"
[[17]][[1]]$main
NULL
[[17]][[1]]$se.mult
[1] 2
[[17]][[1]]$xlim
[1] 1978 2007
[[17]][[1]]$fit
[,1]
[1,] 4.74516129
[2,] 4.64929945
[3,] 4.55343760
[4,] 4.45757576
[5,] 4.36171391
[6,] 4.26585207
[7,] 4.16999022
[8,] 4.07412838
[9,] 3.97826654
[10,] 3.88240469
[11,] 3.78654285
[12,] 3.69068100
[13,] 3.59481916
[14,] 3.49895732
[15,] 3.40309547
[16,] 3.30723363
[17,] 3.21137178
[18,] 3.11550994
[19,] 3.01964809
[20,] 2.92378625
[21,] 2.82792441
[22,] 2.73206256
[23,] 2.63620072
[24,] 2.54033887
[25,] 2.44447703
[26,] 2.34861518
[27,] 2.25275334
[28,] 2.15689150
[29,] 2.06102965
[30,] 1.96516781
[31,] 1.86930596
[32,] 1.77344412
[33,] 1.67758227
[34,] 1.58172043
[35,] 1.48585859
[36,] 1.38999674
[37,] 1.29413490
[38,] 1.19827305
[39,] 1.10241121
[40,] 1.00654936
[41,] 0.91068752
[42,] 0.81482568
[43,] 0.71896383
[44,] 0.62310199
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[82,] -3.01964809
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[84,] -3.21137178
[85,] -3.30723363
[86,] -3.40309547
[87,] -3.49895732
[88,] -3.59481916
[89,] -3.69068100
[90,] -3.78654285
[91,] -3.88240469
[92,] -3.97826654
[93,] -4.07412838
[94,] -4.16999022
[95,] -4.26585207
[96,] -4.36171391
[97,] -4.45757576
[98,] -4.55343760
[99,] -4.64929945
[100,] -4.74516129
[[17]][[1]]$plot.me
[1] TRUE
[[18]]
[[18]][[1]]
[[18]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[18]][[1]]$scale
[1] TRUE
[[18]][[1]]$se
[1] 6.859260 6.634205 6.411948 6.192849 5.977289 5.765693 5.558522 5.356245
[9] 5.159345 4.968320 4.783661 4.605846 4.435334 4.272556 4.117898 3.971690
[17] 3.834204 3.705629 3.586070 3.475540 3.373956 3.281123 3.196756 3.120480
[25] 3.051829 2.990262 2.935205 2.886041 2.842124 2.802830 2.767562 2.735741
[33] 2.706840 2.680414 2.656069 2.633467 2.612367 2.592592 2.574014 2.556575
[41] 2.540282 2.525171 2.511310 2.498809 2.487787 2.478359 2.470647 2.464761
[49] 2.460787 2.458780 2.458780 2.460787 2.464761 2.470647 2.478359 2.487787
[57] 2.498809 2.511310 2.525171 2.540282 2.556575 2.574014 2.592592 2.612367
[65] 2.633467 2.656069 2.680414 2.706840 2.735741 2.767562 2.802830 2.842124
[73] 2.886041 2.935205 2.990262 3.051829 3.120480 3.196756 3.281123 3.373956
[81] 3.475540 3.586070 3.705629 3.834204 3.971690 4.117898 4.272556 4.435334
[89] 4.605846 4.783661 4.968320 5.159345 5.356245 5.558522 5.765693 5.977289
[97] 6.192849 6.411948 6.634205 6.859260
[[18]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[18]][[1]]$xlab
[1] "YEAR"
[[18]][[1]]$ylab
[1] "s(YEAR,1.47)"
[[18]][[1]]$main
NULL
[[18]][[1]]$se.mult
[1] 2
[[18]][[1]]$xlim
[1] 1978 2007
[[18]][[1]]$fit
[,1]
[1,] -6.09833367
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[4,] -5.54937638
[5,] -5.36670734
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[7,] -5.00237581
[8,] -4.82094028
[9,] -4.64015047
[10,] -4.46014472
[11,] -4.28106393
[12,] -4.10304978
[13,] -3.92625040
[14,] -3.75081718
[15,] -3.57690149
[16,] -3.40465330
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[41,] 0.02760652
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[48,] 0.63729188
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[88,] 2.88261777
[89,] 2.93750845
[90,] 2.99263881
[91,] 3.04798591
[92,] 3.10352407
[93,] 3.15922725
[94,] 3.21506963
[95,] 3.27102664
[96,] 3.32707424
[97,] 3.38318846
[98,] 3.43934907
[99,] 3.49554039
[100,] 3.55174708
[[18]][[1]]$plot.me
[1] TRUE
[[19]]
[[19]][[1]]
[[19]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[19]][[1]]$scale
[1] TRUE
[[19]][[1]]$se
[1] 5.07852944 4.97593289 4.87333633 4.77073978 4.66814322 4.56554667
[7] 4.46295011 4.36035356 4.25775701 4.15516045 4.05256390 3.94996734
[13] 3.84737079 3.74477423 3.64217768 3.53958113 3.43698457 3.33438802
[19] 3.23179146 3.12919491 3.02659835 2.92400180 2.82140524 2.71880869
[25] 2.61621214 2.51361558 2.41101903 2.30842247 2.20582592 2.10322936
[31] 2.00063281 1.89803626 1.79543970 1.69284315 1.59024659 1.48765004
[37] 1.38505348 1.28245693 1.17986038 1.07726382 0.97466727 0.87207071
[43] 0.76947416 0.66687760 0.56428105 0.46168450 0.35908794 0.25649139
[49] 0.15389483 0.05129828 0.05129828 0.15389483 0.25649139 0.35908794
[55] 0.46168450 0.56428105 0.66687760 0.76947416 0.87207071 0.97466727
[61] 1.07726382 1.17986038 1.28245693 1.38505348 1.48765004 1.59024659
[67] 1.69284315 1.79543970 1.89803626 2.00063281 2.10322936 2.20582592
[73] 2.30842247 2.41101903 2.51361558 2.61621214 2.71880869 2.82140524
[79] 2.92400180 3.02659835 3.12919491 3.23179146 3.33438802 3.43698457
[85] 3.53958113 3.64217768 3.74477423 3.84737079 3.94996734 4.05256390
[91] 4.15516045 4.25775701 4.36035356 4.46295011 4.56554667 4.66814322
[97] 4.77073978 4.87333633 4.97593289 5.07852944
[[19]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[19]][[1]]$xlab
[1] "YEAR"
[[19]][[1]]$ylab
[1] "s(YEAR,1)"
[[19]][[1]]$main
NULL
[[19]][[1]]$se.mult
[1] 2
[[19]][[1]]$xlim
[1] 1978 2007
[[19]][[1]]$fit
[,1]
[1,] 5.60967742
[2,] 5.49635060
[3,] 5.38302379
[4,] 5.26969697
[5,] 5.15637015
[6,] 5.04304334
[7,] 4.92971652
[8,] 4.81638970
[9,] 4.70306289
[10,] 4.58973607
[11,] 4.47640925
[12,] 4.36308244
[13,] 4.24975562
[14,] 4.13642880
[15,] 4.02310199
[16,] 3.90977517
[17,] 3.79644835
[18,] 3.68312154
[19,] 3.56979472
[20,] 3.45646790
[21,] 3.34314109
[22,] 3.22981427
[23,] 3.11648746
[24,] 3.00316064
[25,] 2.88983382
[26,] 2.77650701
[27,] 2.66318019
[28,] 2.54985337
[29,] 2.43652656
[30,] 2.32319974
[31,] 2.20987292
[32,] 2.09654611
[33,] 1.98321929
[34,] 1.86989247
[35,] 1.75656566
[36,] 1.64323884
[37,] 1.52991202
[38,] 1.41658521
[39,] 1.30325839
[40,] 1.18993157
[41,] 1.07660476
[42,] 0.96327794
[43,] 0.84995112
[44,] 0.73662431
[45,] 0.62329749
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[84,] -3.79644835
[85,] -3.90977517
[86,] -4.02310199
[87,] -4.13642880
[88,] -4.24975562
[89,] -4.36308244
[90,] -4.47640925
[91,] -4.58973607
[92,] -4.70306289
[93,] -4.81638970
[94,] -4.92971652
[95,] -5.04304334
[96,] -5.15637015
[97,] -5.26969697
[98,] -5.38302379
[99,] -5.49635060
[100,] -5.60967742
[[19]][[1]]$plot.me
[1] TRUE
[[20]]
[[20]][[1]]
[[20]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[20]][[1]]$scale
[1] TRUE
[[20]][[1]]$se
[1] 5.2583631 5.1485273 5.0388404 4.9293144 4.8199618 4.7107958 4.6018305
[8] 4.4930793 4.3845554 4.2762721 4.1682419 4.0604762 3.9529858 3.8457804
[15] 3.7388685 3.6322574 3.5259534 3.4199615 3.3142855 3.2089283 3.1038921
[22] 2.9991779 2.8947869 2.7907198 2.6869778 2.5835623 2.4804766 2.3777252
[29] 2.2753152 2.1732572 2.0715667 1.9702643 1.8693783 1.7689472 1.6690220
[36] 1.5696692 1.4709781 1.3730668 1.2760916 1.1802630 1.0858677 0.9932986
[43] 0.9031039 0.8160614 0.7332860 0.6563864 0.5876694 0.5303226 0.4883656
[50] 0.4659721 0.4659721 0.4883656 0.5303226 0.5876694 0.6563864 0.7332860
[57] 0.8160614 0.9031039 0.9932986 1.0858677 1.1802630 1.2760916 1.3730668
[64] 1.4709781 1.5696692 1.6690220 1.7689472 1.8693783 1.9702643 2.0715667
[71] 2.1732572 2.2753152 2.3777252 2.4804766 2.5835623 2.6869778 2.7907198
[78] 2.8947869 2.9991779 3.1038921 3.2089283 3.3142855 3.4199615 3.5259534
[85] 3.6322574 3.7388685 3.8457804 3.9529858 4.0604762 4.1682419 4.2762721
[92] 4.3845554 4.4930793 4.6018305 4.7107958 4.8199618 4.9293144 5.0388404
[99] 5.1485273 5.2583631
[[20]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[20]][[1]]$xlab
[1] "YEAR"
[[20]][[1]]$ylab
[1] "s(YEAR,1.02)"
[[20]][[1]]$main
NULL
[[20]][[1]]$se.mult
[1] 2
[[20]][[1]]$xlim
[1] 1978 2007
[[20]][[1]]$fit
[,1]
[1,] 8.94010031
[2,] 8.76117354
[3,] 8.58224519
[4,] 8.40331372
[5,] 8.22437751
[6,] 8.04543437
[7,] 7.86648168
[8,] 7.68751676
[9,] 7.50853678
[10,] 7.32953849
[11,] 7.15051853
[12,] 6.97147358
[13,] 6.79240007
[14,] 6.61329437
[15,] 6.43415284
[16,] 6.25497184
[17,] 6.07574770
[18,] 5.89647679
[19,] 5.71715548
[20,] 5.53778031
[21,] 5.35834787
[22,] 5.17885476
[23,] 4.99929779
[24,] 4.81967397
[25,] 4.63998031
[26,] 4.46021397
[27,] 4.28037247
[28,] 4.10045339
[29,] 3.92045436
[30,] 3.74037339
[31,] 3.56020874
[32,] 3.37995865
[33,] 3.19962160
[34,] 3.01919651
[35,] 2.83868233
[36,] 2.65807809
[37,] 2.47738327
[38,] 2.29659751
[39,] 2.11572050
[40,] 1.93475219
[41,] 1.75369289
[42,] 1.57254291
[43,] 1.39130268
[44,] 1.20997305
[45,] 1.02855494
[46,] 0.84704927
[47,] 0.66545729
[48,] 0.48378041
[49,] 0.30202007
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[80,] -5.36258357
[81,] -5.54589644
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[83,] -5.91256715
[84,] -6.09592217
[85,] -6.27928863
[86,] -6.46266532
[87,] -6.64605107
[88,] -6.82944481
[89,] -7.01284558
[90,] -7.19625242
[91,] -7.37966441
[92,] -7.56308081
[93,] -7.74650085
[94,] -7.92992382
[95,] -8.11334912
[96,] -8.29677623
[97,] -8.48020463
[98,] -8.66363389
[99,] -8.84706372
[100,] -9.03049384
[[20]][[1]]$plot.me
[1] TRUE
[[21]]
[[21]][[1]]
[[21]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[21]][[1]]$scale
[1] TRUE
[[21]][[1]]$se
[1] 4.341371 4.161236 3.983835 3.809621 3.639087 3.472801 3.311392 3.155523
[9] 3.005899 2.863260 2.728359 2.601939 2.484719 2.377356 2.280411 2.194304
[17] 2.119285 2.055386 2.002397 1.959870 1.927115 1.903227 1.887142 1.877704
[25] 1.873690 1.873881 1.877136 1.882394 1.888685 1.895194 1.901251 1.906294
[33] 1.909898 1.911792 1.911806 1.909858 1.905997 1.900359 1.893132 1.884582
[41] 1.875045 1.864879 1.854464 1.844212 1.834525 1.825774 1.818309 1.812432
[49] 1.808378 1.806306 1.806306 1.808378 1.812432 1.818309 1.825774 1.834525
[57] 1.844212 1.854464 1.864879 1.875045 1.884582 1.893132 1.900359 1.905997
[65] 1.909858 1.911806 1.911792 1.909898 1.906294 1.901251 1.895194 1.888685
[73] 1.882394 1.877136 1.873881 1.873690 1.877704 1.887142 1.903227 1.927115
[81] 1.959870 2.002397 2.055386 2.119285 2.194304 2.280411 2.377356 2.484719
[89] 2.601939 2.728359 2.863260 3.005899 3.155523 3.311392 3.472801 3.639087
[97] 3.809621 3.983835 4.161236 4.341371
[[21]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[21]][[1]]$xlab
[1] "YEAR"
[[21]][[1]]$ylab
[1] "s(YEAR,2.02)"
[[21]][[1]]$main
NULL
[[21]][[1]]$se.mult
[1] 2
[[21]][[1]]$xlim
[1] 1978 2007
[[21]][[1]]$fit
[,1]
[1,] -3.32027435
[2,] -3.14684096
[3,] -2.97348871
[4,] -2.80029870
[5,] -2.62735401
[6,] -2.45476831
[7,] -2.28267970
[8,] -2.11122698
[9,] -1.94055895
[10,] -1.77084842
[11,] -1.60227179
[12,] -1.43500693
[13,] -1.26924448
[14,] -1.10518147
[15,] -0.94301504
[16,] -0.78294486
[17,] -0.62517444
[18,] -0.46990760
[19,] -0.31734753
[20,] -0.16769441
[21,] -0.02114747
[22,] 0.12209436
[23,] 0.26183877
[24,] 0.39789974
[25,] 0.53009154
[26,] 0.65823293
[27,] 0.78215594
[28,] 0.90169507
[29,] 1.01668614
[30,] 1.12697967
[31,] 1.23243506
[32,] 1.33291193
[33,] 1.42827929
[34,] 1.51842308
[35,] 1.60323105
[36,] 1.68259415
[37,] 1.75642273
[38,] 1.82463449
[39,] 1.88714757
[40,] 1.94389372
[41,] 1.99482030
[42,] 2.03987547
[43,] 2.07901299
[44,] 2.11220662
[45,] 2.13943462
[46,] 2.16067642
[47,] 2.17592735
[48,] 2.18519436
[49,] 2.18848466
[50,] 2.18581332
[51,] 2.17721245
[52,] 2.16271647
[53,] 2.14236186
[54,] 2.11620087
[55,] 2.08429297
[56,] 2.04669785
[57,] 2.00348436
[58,] 1.95473381
[59,] 1.90052846
[60,] 1.84095359
[61,] 1.77610793
[62,] 1.70609397
[63,] 1.63101467
[64,] 1.55098200
[65,] 1.46611580
[66,] 1.37653617
[67,] 1.28236684
[68,] 1.18374121
[69,] 1.08079429
[70,] 0.97366183
[71,] 0.86248681
[72,] 0.74741621
[73,] 0.62859708
[74,] 0.50617965
[75,] 0.38031930
[76,] 0.25117193
[77,] 0.11889404
[78,] -0.01635439
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[80,] -0.29511824
[81,] -0.43831087
[82,] -0.58382799
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[84,] -0.88118800
[85,] -1.03271118
[86,] -1.18591911
[87,] -1.34065443
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[89,] -1.65410634
[90,] -1.81252872
[91,] -1.97189187
[92,] -2.13206627
[93,] -2.29292382
[94,] -2.45433914
[95,] -2.61620552
[96,] -2.77842399
[97,] -2.94089610
[98,] -3.10354109
[99,] -3.26630041
[100,] -3.42911689
[[21]][[1]]$plot.me
[1] TRUE
[[22]]
[[22]][[1]]
[[22]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[22]][[1]]$scale
[1] TRUE
[[22]][[1]]$se
[1] 7.80651902 7.64881157 7.49110411 7.33339666 7.17568920 7.01798175
[7] 6.86027429 6.70256684 6.54485938 6.38715193 6.22944447 6.07173702
[13] 5.91402956 5.75632211 5.59861465 5.44090720 5.28319974 5.12549229
[19] 4.96778483 4.81007738 4.65236992 4.49466247 4.33695501 4.17924756
[25] 4.02154010 3.86383265 3.70612519 3.54841774 3.39071028 3.23300283
[31] 3.07529537 2.91758792 2.75988046 2.60217301 2.44446555 2.28675810
[37] 2.12905064 1.97134319 1.81363573 1.65592828 1.49822082 1.34051337
[43] 1.18280591 1.02509846 0.86739100 0.70968355 0.55197609 0.39426864
[49] 0.23656118 0.07885373 0.07885373 0.23656118 0.39426864 0.55197609
[55] 0.70968355 0.86739100 1.02509846 1.18280591 1.34051337 1.49822082
[61] 1.65592828 1.81363573 1.97134319 2.12905064 2.28675810 2.44446555
[67] 2.60217301 2.75988046 2.91758792 3.07529537 3.23300283 3.39071028
[73] 3.54841774 3.70612519 3.86383265 4.02154010 4.17924756 4.33695501
[79] 4.49466247 4.65236992 4.81007738 4.96778483 5.12549229 5.28319974
[85] 5.44090720 5.59861465 5.75632211 5.91402956 6.07173702 6.22944447
[91] 6.38715193 6.54485938 6.70256684 6.86027429 7.01798175 7.17568920
[97] 7.33339666 7.49110411 7.64881157 7.80651902
[[22]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[22]][[1]]$xlab
[1] "YEAR"
[[22]][[1]]$ylab
[1] "s(YEAR,1)"
[[22]][[1]]$main
NULL
[[22]][[1]]$se.mult
[1] 2
[[22]][[1]]$xlim
[1] 1978 2007
[[22]][[1]]$fit
[,1]
[1,] -7.54838710
[2,] -7.39589443
[3,] -7.24340176
[4,] -7.09090909
[5,] -6.93841642
[6,] -6.78592375
[7,] -6.63343109
[8,] -6.48093842
[9,] -6.32844575
[10,] -6.17595308
[11,] -6.02346041
[12,] -5.87096774
[13,] -5.71847507
[14,] -5.56598240
[15,] -5.41348974
[16,] -5.26099707
[17,] -5.10850440
[18,] -4.95601173
[19,] -4.80351906
[20,] -4.65102639
[21,] -4.49853372
[22,] -4.34604106
[23,] -4.19354839
[24,] -4.04105572
[25,] -3.88856305
[26,] -3.73607038
[27,] -3.58357771
[28,] -3.43108504
[29,] -3.27859238
[30,] -3.12609971
[31,] -2.97360704
[32,] -2.82111437
[33,] -2.66862170
[34,] -2.51612903
[35,] -2.36363636
[36,] -2.21114370
[37,] -2.05865103
[38,] -1.90615836
[39,] -1.75366569
[40,] -1.60117302
[41,] -1.44868035
[42,] -1.29618768
[43,] -1.14369501
[44,] -0.99120235
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[55,] 0.68621701
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[57,] 0.99120235
[58,] 1.14369501
[59,] 1.29618768
[60,] 1.44868035
[61,] 1.60117302
[62,] 1.75366569
[63,] 1.90615836
[64,] 2.05865103
[65,] 2.21114370
[66,] 2.36363636
[67,] 2.51612903
[68,] 2.66862170
[69,] 2.82111437
[70,] 2.97360704
[71,] 3.12609971
[72,] 3.27859238
[73,] 3.43108504
[74,] 3.58357771
[75,] 3.73607038
[76,] 3.88856305
[77,] 4.04105572
[78,] 4.19354839
[79,] 4.34604106
[80,] 4.49853372
[81,] 4.65102639
[82,] 4.80351906
[83,] 4.95601173
[84,] 5.10850440
[85,] 5.26099707
[86,] 5.41348974
[87,] 5.56598240
[88,] 5.71847507
[89,] 5.87096774
[90,] 6.02346041
[91,] 6.17595308
[92,] 6.32844575
[93,] 6.48093842
[94,] 6.63343109
[95,] 6.78592375
[96,] 6.93841642
[97,] 7.09090909
[98,] 7.24340176
[99,] 7.39589443
[100,] 7.54838710
[[22]][[1]]$plot.me
[1] TRUE
[[23]]
[[23]][[1]]
[[23]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[23]][[1]]$scale
[1] TRUE
[[23]][[1]]$se
[1] 3.115397 2.987926 2.862369 2.739037 2.618270 2.500457 2.386030 2.275443
[9] 2.169176 2.067734 1.971629 1.881369 1.797441 1.720296 1.650319 1.587807
[17] 1.532941 1.485765 1.446160 1.413851 1.388400 1.369219 1.355611 1.346806
[25] 1.341982 1.340308 1.341003 1.343328 1.346605 1.350258 1.353807 1.356844
[33] 1.359058 1.360243 1.360260 1.359037 1.356589 1.352993 1.348362 1.342863
[41] 1.336714 1.330145 1.323404 1.316759 1.310475 1.304794 1.299945 1.296126
[49] 1.293491 1.292144 1.292144 1.293491 1.296126 1.299945 1.304794 1.310475
[57] 1.316759 1.323404 1.330145 1.336714 1.342863 1.348362 1.352993 1.356589
[65] 1.359037 1.360260 1.360243 1.359058 1.356844 1.353807 1.350258 1.346605
[73] 1.343328 1.341003 1.340308 1.341982 1.346806 1.355611 1.369219 1.388400
[81] 1.413851 1.446160 1.485765 1.532941 1.587807 1.650319 1.720296 1.797441
[89] 1.881369 1.971629 2.067734 2.169176 2.275443 2.386030 2.500457 2.618270
[97] 2.739037 2.862369 2.987926 3.115397
[[23]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[23]][[1]]$xlab
[1] "YEAR"
[[23]][[1]]$ylab
[1] "s(YEAR,1.98)"
[[23]][[1]]$main
NULL
[[23]][[1]]$se.mult
[1] 2
[[23]][[1]]$xlim
[1] 1978 2007
[[23]][[1]]$fit
[,1]
[1,] -1.83491915
[2,] -1.82428644
[3,] -1.81366140
[4,] -1.80305171
[5,] -1.79246514
[6,] -1.78191116
[7,] -1.77140058
[8,] -1.76094423
[9,] -1.75055250
[10,] -1.74023470
[11,] -1.72999995
[12,] -1.71985692
[13,] -1.70981018
[14,] -1.69986226
[15,] -1.69001558
[16,] -1.68026834
[17,] -1.67061235
[18,] -1.66103890
[19,] -1.65153724
[20,] -1.64208662
[21,] -1.63266320
[22,] -1.62324273
[23,] -1.61379217
[24,] -1.60427003
[25,] -1.59463449
[26,] -1.58483937
[27,] -1.57482566
[28,] -1.56453201
[29,] -1.55389597
[30,] -1.54284366
[31,] -1.53129421
[32,] -1.51916658
[33,] -1.50637375
[34,] -1.49281781
[35,] -1.47839972
[36,] -1.46301882
[37,] -1.44656473
[38,] -1.42892341
[39,] -1.40998065
[40,] -1.38961757
[41,] -1.36770993
[42,] -1.34413322
[43,] -1.31876203
[44,] -1.29146782
[45,] -1.26212132
[46,] -1.23059336
[47,] -1.19675579
[48,] -1.16048124
[49,] -1.12164238
[50,] -1.08011448
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[52,] -0.98851609
[53,] -0.93821039
[54,] -0.88475469
[55,] -0.82804696
[56,] -0.76798545
[57,] -0.70447764
[58,] -0.63744379
[59,] -0.56680505
[60,] -0.49248694
[61,] -0.41443441
[62,] -0.33259774
[63,] -0.24692818
[64,] -0.15739425
[65,] -0.06397953
[66,] 0.03333183
[67,] 0.13454675
[68,] 0.23964831
[69,] 0.34861563
[70,] 0.46142548
[71,] 0.57803201
[72,] 0.69837691
[73,] 0.82240154
[74,] 0.95003444
[75,] 1.08118309
[76,] 1.21575296
[77,] 1.35364572
[78,] 1.49474207
[79,] 1.63891559
[80,] 1.78603941
[81,] 1.93597493
[82,] 2.08857131
[83,] 2.24367713
[84,] 2.40113787
[85,] 2.56078888
[86,] 2.72246347
[87,] 2.88599482
[88,] 3.05121455
[89,] 3.21795327
[90,] 3.38604159
[91,] 3.55531400
[92,] 3.72561280
[93,] 3.89678117
[94,] 4.06866520
[95,] 4.24113059
[96,] 4.41405120
[97,] 4.58730150
[98,] 4.76077773
[99,] 4.93440343
[100,] 5.10810387
[[23]][[1]]$plot.me
[1] TRUE
[[24]]
[[24]][[1]]
[[24]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[24]][[1]]$scale
[1] TRUE
[[24]][[1]]$se
[1] 5.36077697 5.25247845 5.14417992 5.03588140 4.92758287 4.81928435
[7] 4.71098582 4.60268730 4.49438877 4.38609025 4.27779172 4.16949320
[13] 4.06119468 3.95289615 3.84459763 3.73629910 3.62800058 3.51970205
[19] 3.41140353 3.30310500 3.19480648 3.08650795 2.97820943 2.86991090
[25] 2.76161238 2.65331385 2.54501533 2.43671681 2.32841828 2.22011976
[31] 2.11182123 2.00352271 1.89522418 1.78692566 1.67862713 1.57032861
[37] 1.46203008 1.35373156 1.24543303 1.13713451 1.02883598 0.92053746
[43] 0.81223894 0.70394041 0.59564189 0.48734336 0.37904484 0.27074631
[49] 0.16244779 0.05414927 0.05414927 0.16244779 0.27074631 0.37904484
[55] 0.48734336 0.59564189 0.70394041 0.81223894 0.92053746 1.02883598
[61] 1.13713451 1.24543303 1.35373156 1.46203008 1.57032861 1.67862713
[67] 1.78692566 1.89522418 2.00352271 2.11182123 2.22011976 2.32841828
[73] 2.43671681 2.54501533 2.65331385 2.76161238 2.86991090 2.97820943
[79] 3.08650795 3.19480648 3.30310500 3.41140353 3.51970205 3.62800058
[85] 3.73629910 3.84459763 3.95289615 4.06119468 4.16949320 4.27779172
[91] 4.38609025 4.49438877 4.60268730 4.71098582 4.81928435 4.92758287
[97] 5.03588140 5.14417992 5.25247845 5.36077697
[[24]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[24]][[1]]$xlab
[1] "YEAR"
[[24]][[1]]$ylab
[1] "s(YEAR,1)"
[[24]][[1]]$main
NULL
[[24]][[1]]$se.mult
[1] 2
[[24]][[1]]$xlim
[1] 1978 2007
[[24]][[1]]$fit
[,1]
[1,] -5.54838710
[2,] -5.43629847
[3,] -5.32420984
[4,] -5.21212121
[5,] -5.10003258
[6,] -4.98794396
[7,] -4.87585533
[8,] -4.76376670
[9,] -4.65167807
[10,] -4.53958944
[11,] -4.42750081
[12,] -4.31541219
[13,] -4.20332356
[14,] -4.09123493
[15,] -3.97914630
[16,] -3.86705767
[17,] -3.75496905
[18,] -3.64288042
[19,] -3.53079179
[20,] -3.41870316
[21,] -3.30661453
[22,] -3.19452590
[23,] -3.08243728
[24,] -2.97034865
[25,] -2.85826002
[26,] -2.74617139
[27,] -2.63408276
[28,] -2.52199413
[29,] -2.40990551
[30,] -2.29781688
[31,] -2.18572825
[32,] -2.07363962
[33,] -1.96155099
[34,] -1.84946237
[35,] -1.73737374
[36,] -1.62528511
[37,] -1.51319648
[38,] -1.40110785
[39,] -1.28901922
[40,] -1.17693060
[41,] -1.06484197
[42,] -0.95275334
[43,] -0.84066471
[44,] -0.72857608
[45,] -0.61648746
[46,] -0.50439883
[47,] -0.39231020
[48,] -0.28022157
[49,] -0.16813294
[50,] -0.05604431
[51,] 0.05604431
[52,] 0.16813294
[53,] 0.28022157
[54,] 0.39231020
[55,] 0.50439883
[56,] 0.61648746
[57,] 0.72857608
[58,] 0.84066471
[59,] 0.95275334
[60,] 1.06484197
[61,] 1.17693060
[62,] 1.28901922
[63,] 1.40110785
[64,] 1.51319648
[65,] 1.62528511
[66,] 1.73737374
[67,] 1.84946237
[68,] 1.96155099
[69,] 2.07363962
[70,] 2.18572825
[71,] 2.29781688
[72,] 2.40990551
[73,] 2.52199413
[74,] 2.63408276
[75,] 2.74617139
[76,] 2.85826002
[77,] 2.97034865
[78,] 3.08243728
[79,] 3.19452590
[80,] 3.30661453
[81,] 3.41870316
[82,] 3.53079179
[83,] 3.64288042
[84,] 3.75496905
[85,] 3.86705767
[86,] 3.97914630
[87,] 4.09123493
[88,] 4.20332356
[89,] 4.31541219
[90,] 4.42750081
[91,] 4.53958944
[92,] 4.65167807
[93,] 4.76376670
[94,] 4.87585533
[95,] 4.98794396
[96,] 5.10003258
[97,] 5.21212121
[98,] 5.32420984
[99,] 5.43629847
[100,] 5.54838710
[[24]][[1]]$plot.me
[1] TRUE
[[25]]
[[25]][[1]]
[[25]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[25]][[1]]$scale
[1] TRUE
[[25]][[1]]$se
[1] 3.67463662 3.60040153 3.52616645 3.45193137 3.37769628 3.30346120
[7] 3.22922612 3.15499103 3.08075595 3.00652087 2.93228578 2.85805070
[13] 2.78381562 2.70958054 2.63534545 2.56111037 2.48687529 2.41264020
[19] 2.33840512 2.26417004 2.18993495 2.11569987 2.04146479 1.96722970
[25] 1.89299462 1.81875954 1.74452445 1.67028937 1.59605429 1.52181920
[31] 1.44758412 1.37334904 1.29911396 1.22487887 1.15064379 1.07640871
[37] 1.00217362 0.92793854 0.85370346 0.77946837 0.70523329 0.63099821
[43] 0.55676312 0.48252804 0.40829296 0.33405787 0.25982279 0.18558771
[49] 0.11135263 0.03711754 0.03711754 0.11135263 0.18558771 0.25982279
[55] 0.33405787 0.40829296 0.48252804 0.55676312 0.63099821 0.70523329
[61] 0.77946837 0.85370346 0.92793854 1.00217362 1.07640871 1.15064379
[67] 1.22487887 1.29911396 1.37334904 1.44758412 1.52181920 1.59605429
[73] 1.67028937 1.74452445 1.81875954 1.89299462 1.96722970 2.04146479
[79] 2.11569987 2.18993495 2.26417004 2.33840512 2.41264020 2.48687529
[85] 2.56111037 2.63534545 2.70958054 2.78381562 2.85805070 2.93228578
[91] 3.00652087 3.08075595 3.15499103 3.22922612 3.30346120 3.37769628
[97] 3.45193137 3.52616645 3.60040153 3.67463662
[[25]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[25]][[1]]$xlab
[1] "YEAR"
[[25]][[1]]$ylab
[1] "s(YEAR,1)"
[[25]][[1]]$main
NULL
[[25]][[1]]$se.mult
[1] 2
[[25]][[1]]$xlim
[1] 1978 2007
[[25]][[1]]$fit
[,1]
[1,] -9.33225806
[2,] -9.14372760
[3,] -8.95519713
[4,] -8.76666667
[5,] -8.57813620
[6,] -8.38960573
[7,] -8.20107527
[8,] -8.01254480
[9,] -7.82401434
[10,] -7.63548387
[11,] -7.44695341
[12,] -7.25842294
[13,] -7.06989247
[14,] -6.88136201
[15,] -6.69283154
[16,] -6.50430108
[17,] -6.31577061
[18,] -6.12724014
[19,] -5.93870968
[20,] -5.75017921
[21,] -5.56164875
[22,] -5.37311828
[23,] -5.18458781
[24,] -4.99605735
[25,] -4.80752688
[26,] -4.61899642
[27,] -4.43046595
[28,] -4.24193548
[29,] -4.05340502
[30,] -3.86487455
[31,] -3.67634409
[32,] -3.48781362
[33,] -3.29928315
[34,] -3.11075269
[35,] -2.92222222
[36,] -2.73369176
[37,] -2.54516129
[38,] -2.35663082
[39,] -2.16810036
[40,] -1.97956989
[41,] -1.79103943
[42,] -1.60250896
[43,] -1.41397849
[44,] -1.22544803
[45,] -1.03691756
[46,] -0.84838710
[47,] -0.65985663
[48,] -0.47132616
[49,] -0.28279570
[50,] -0.09426523
[51,] 0.09426523
[52,] 0.28279570
[53,] 0.47132616
[54,] 0.65985663
[55,] 0.84838710
[56,] 1.03691756
[57,] 1.22544803
[58,] 1.41397849
[59,] 1.60250896
[60,] 1.79103943
[61,] 1.97956989
[62,] 2.16810036
[63,] 2.35663082
[64,] 2.54516129
[65,] 2.73369176
[66,] 2.92222222
[67,] 3.11075269
[68,] 3.29928315
[69,] 3.48781362
[70,] 3.67634409
[71,] 3.86487455
[72,] 4.05340502
[73,] 4.24193548
[74,] 4.43046595
[75,] 4.61899642
[76,] 4.80752688
[77,] 4.99605735
[78,] 5.18458781
[79,] 5.37311828
[80,] 5.56164875
[81,] 5.75017921
[82,] 5.93870968
[83,] 6.12724014
[84,] 6.31577061
[85,] 6.50430108
[86,] 6.69283154
[87,] 6.88136201
[88,] 7.06989247
[89,] 7.25842294
[90,] 7.44695341
[91,] 7.63548387
[92,] 7.82401434
[93,] 8.01254480
[94,] 8.20107527
[95,] 8.38960573
[96,] 8.57813620
[97,] 8.76666667
[98,] 8.95519713
[99,] 9.14372760
[100,] 9.33225806
[[25]][[1]]$plot.me
[1] TRUE
[[26]]
[[26]][[1]]
[[26]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[26]][[1]]$scale
[1] TRUE
[[26]][[1]]$se
[1] 7.633906 7.398010 7.164850 6.934758 6.708079 6.485200 6.266536 6.052507
[9] 5.843540 5.640075 5.442541 5.251353 5.066911 4.889586 4.719709 4.557570
[17] 4.403405 4.257391 4.119636 3.990179 3.868986 3.755940 3.650850 3.553462
[25] 3.463448 3.380416 3.303948 3.233582 3.168826 3.109196 3.054222 3.003436
[33] 2.956406 2.912759 2.872160 2.834312 2.799000 2.766065 2.735385 2.706900
[41] 2.680612 2.656549 2.634767 2.615364 2.598450 2.584128 2.572510 2.563703
[49] 2.557783 2.554805 2.554805 2.557783 2.563703 2.572510 2.584128 2.598450
[57] 2.615364 2.634767 2.656549 2.680612 2.706900 2.735385 2.766065 2.799000
[65] 2.834312 2.872160 2.912759 2.956406 3.003436 3.054222 3.109196 3.168826
[73] 3.233582 3.303948 3.380416 3.463448 3.553462 3.650850 3.755940 3.868986
[81] 3.990179 4.119636 4.257391 4.403405 4.557570 4.719709 4.889586 5.066911
[89] 5.251353 5.442541 5.640075 5.843540 6.052507 6.266536 6.485200 6.708079
[97] 6.934758 7.164850 7.398010 7.633906
[[26]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[26]][[1]]$xlab
[1] "YEAR"
[[26]][[1]]$ylab
[1] "s(YEAR,1.37)"
[[26]][[1]]$main
NULL
[[26]][[1]]$se.mult
[1] 2
[[26]][[1]]$xlim
[1] 1978 2007
[[26]][[1]]$fit
[,1]
[1,] -7.52419185
[2,] -7.32005361
[3,] -7.11596461
[4,] -6.91197408
[5,] -6.70813240
[6,] -6.50450813
[7,] -6.30118431
[8,] -6.09824440
[9,] -5.89577746
[10,] -5.69388597
[11,] -5.49267441
[12,] -5.29224796
[13,] -5.09271774
[14,] -4.89419785
[15,] -4.69680242
[16,] -4.50064559
[17,] -4.30584153
[18,] -4.11250443
[19,] -3.92074741
[20,] -3.73067845
[21,] -3.54240396
[22,] -3.35603001
[23,] -3.17165590
[24,] -2.98937442
[25,] -2.80927809
[26,] -2.63145537
[27,] -2.45598272
[28,] -2.28293440
[29,] -2.11238351
[30,] -1.94439085
[31,] -1.77900970
[32,] -1.61629319
[33,] -1.45628700
[34,] -1.29902338
[35,] -1.14453315
[36,] -0.99284476
[37,] -0.84397217
[38,] -0.69792391
[39,] -0.55470817
[40,] -0.41432373
[41,] -0.27675860
[42,] -0.14200021
[43,] -0.01003249
[44,] 0.11917321
[45,] 0.24564836
[46,] 0.36942508
[47,] 0.49054428
[48,] 0.60905326
[49,] 0.72499949
[50,] 0.83843405
[51,] 0.94941590
[52,] 1.05800504
[53,] 1.16426223
[54,] 1.26825377
[55,] 1.37004855
[56,] 1.46971550
[57,] 1.56732563
[58,] 1.66295282
[59,] 1.75667116
[60,] 1.84855499
[61,] 1.93867978
[62,] 2.02712136
[63,] 2.11395547
[64,] 2.19925717
[65,] 2.28310093
[66,] 2.36556116
[67,] 2.44671133
[68,] 2.52662235
[69,] 2.60536471
[70,] 2.68300853
[71,] 2.75962040
[72,] 2.83526494
[73,] 2.91000673
[74,] 2.98390780
[75,] 3.05702598
[76,] 3.12941873
[77,] 3.20114253
[78,] 3.27224876
[79,] 3.34278703
[80,] 3.41280682
[81,] 3.48235387
[82,] 3.55147005
[83,] 3.62019704
[84,] 3.68857495
[85,] 3.75663885
[86,] 3.82442279
[87,] 3.89196046
[88,] 3.95928151
[89,] 4.02641290
[90,] 4.09338152
[91,] 4.16021223
[92,] 4.22692580
[93,] 4.29354253
[94,] 4.36008212
[95,] 4.42656022
[96,] 4.49299079
[97,] 4.55938774
[98,] 4.62576218
[99,] 4.69212175
[100,] 4.75847389
[[26]][[1]]$plot.me
[1] TRUE
[[27]]
[[27]][[1]]
[[27]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[27]][[1]]$scale
[1] TRUE
[[27]][[1]]$se
[1] 4.458032 4.262790 4.070639 3.882120 3.697830 3.518458 3.344777 3.177607
[9] 3.017825 2.866361 2.724162 2.592167 2.471276 2.362302 2.265907 2.182549
[17] 2.112423 2.055408 2.011039 1.978528 1.956783 1.944465 1.940084 1.942095
[25] 1.948936 1.959111 1.971281 1.984240 1.996924 2.008479 2.018231 2.025640
[33] 2.030325 2.032093 2.030855 2.026627 2.019577 2.009968 1.998125 1.984464
[41] 1.969486 1.953715 1.937706 1.922049 1.907323 1.894068 1.882788 1.873922
[49] 1.867810 1.864690 1.864690 1.867810 1.873922 1.882788 1.894068 1.907323
[57] 1.922049 1.937706 1.953715 1.969486 1.984464 1.998125 2.009968 2.019577
[65] 2.026627 2.030855 2.032093 2.030325 2.025640 2.018231 2.008479 1.996924
[73] 1.984240 1.971281 1.959111 1.948936 1.942095 1.940084 1.944465 1.956783
[81] 1.978528 2.011039 2.055408 2.112423 2.182549 2.265907 2.362302 2.471276
[89] 2.592167 2.724162 2.866361 3.017825 3.177607 3.344777 3.518458 3.697830
[97] 3.882120 4.070639 4.262790 4.458032
[[27]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[27]][[1]]$xlab
[1] "YEAR"
[[27]][[1]]$ylab
[1] "s(YEAR,2.19)"
[[27]][[1]]$main
NULL
[[27]][[1]]$se.mult
[1] 2
[[27]][[1]]$xlim
[1] 1978 2007
[[27]][[1]]$fit
[,1]
[1,] -4.05882752
[2,] -3.85152799
[3,] -3.64437807
[4,] -3.43752739
[5,] -3.23112901
[6,] -3.02539004
[7,] -2.82056082
[8,] -2.61689291
[9,] -2.41465357
[10,] -2.21414786
[11,] -2.01568642
[12,] -1.81958147
[13,] -1.62615847
[14,] -1.43574953
[15,] -1.24868675
[16,] -1.06529823
[17,] -0.88590601
[18,] -0.71083167
[19,] -0.54039179
[20,] -0.37487850
[21,] -0.21457639
[22,] -0.05976874
[23,] 0.08928924
[24,] 0.23236917
[25,] 0.36924378
[26,] 0.49970176
[27,] 0.62357873
[28,] 0.74071893
[29,] 0.85097095
[30,] 0.95422999
[31,] 1.05041956
[32,] 1.13946385
[33,] 1.22131425
[34,] 1.29597144
[35,] 1.36344128
[36,] 1.42373806
[37,] 1.47692722
[38,] 1.52309347
[39,] 1.56232257
[40,] 1.59473200
[41,] 1.62047548
[42,] 1.63970870
[43,] 1.65259828
[44,] 1.65935022
[45,] 1.66017935
[46,] 1.65530232
[47,] 1.64496012
[48,] 1.62941153
[49,] 1.60891578
[50,] 1.58374001
[51,] 1.55416870
[52,] 1.52048860
[53,] 1.48298731
[54,] 1.44195874
[55,] 1.39769968
[56,] 1.35050686
[57,] 1.30067414
[58,] 1.24849144
[59,] 1.19424840
[60,] 1.13823119
[61,] 1.08071073
[62,] 1.02195369
[63,] 0.96222571
[64,] 0.90177386
[65,] 0.84082899
[66,] 0.77962136
[67,] 0.71836988
[68,] 0.65726321
[69,] 0.59648505
[70,] 0.53621572
[71,] 0.47660368
[72,] 0.41777978
[73,] 0.35987440
[74,] 0.30299830
[75,] 0.24722990
[76,] 0.19264458
[77,] 0.13931135
[78,] 0.08726429
[79,] 0.03652560
[80,] -0.01288341
[81,] -0.06096336
[82,] -0.10773789
[83,] -0.15323170
[84,] -0.19747696
[85,] -0.24053016
[86,] -0.28245273
[87,] -0.32330719
[88,] -0.36316924
[89,] -0.40212336
[90,] -0.44025421
[91,] -0.47764861
[92,] -0.51439769
[93,] -0.55059311
[94,] -0.58632546
[95,] -0.62167825
[96,] -0.65673203
[97,] -0.69156698
[98,] -0.72625042
[99,] -0.76083353
[100,] -0.79536648
[[27]][[1]]$plot.me
[1] TRUE
[[28]]
[[28]][[1]]
[[28]][[1]]$x
[1] 1978.000 1978.293 1978.586 1978.879 1979.172 1979.465 1979.758 1980.051
[9] 1980.343 1980.636 1980.929 1981.222 1981.515 1981.808 1982.101 1982.394
[17] 1982.687 1982.980 1983.273 1983.566 1983.859 1984.152 1984.444 1984.737
[25] 1985.030 1985.323 1985.616 1985.909 1986.202 1986.495 1986.788 1987.081
[33] 1987.374 1987.667 1987.960 1988.253 1988.545 1988.838 1989.131 1989.424
[41] 1989.717 1990.010 1990.303 1990.596 1990.889 1991.182 1991.475 1991.768
[49] 1992.061 1992.354 1992.646 1992.939 1993.232 1993.525 1993.818 1994.111
[57] 1994.404 1994.697 1994.990 1995.283 1995.576 1995.869 1996.162 1996.455
[65] 1996.747 1997.040 1997.333 1997.626 1997.919 1998.212 1998.505 1998.798
[73] 1999.091 1999.384 1999.677 1999.970 2000.263 2000.556 2000.848 2001.141
[81] 2001.434 2001.727 2002.020 2002.313 2002.606 2002.899 2003.192 2003.485
[89] 2003.778 2004.071 2004.364 2004.657 2004.949 2005.242 2005.535 2005.828
[97] 2006.121 2006.414 2006.707 2007.000
[[28]][[1]]$scale
[1] TRUE
[[28]][[1]]$se
[1] 10.487335 10.234514 9.983272 9.733759 9.486125 9.240537 8.997169
[8] 8.756191 8.517775 8.282091 8.049302 7.819562 7.593014 7.369790
[15] 7.150007 6.933766 6.721152 6.512232 6.307056 6.105658 5.908057
[22] 5.714254 5.524238 5.337992 5.155487 4.976689 4.801568 4.630100
[29] 4.462261 4.298051 4.137493 3.980627 3.827533 3.678339 3.533217
[36] 3.392390 3.256161 3.124907 2.999078 2.879219 2.765980 2.660098
[43] 2.562400 2.473805 2.395289 2.327842 2.272442 2.229989 2.201231
[50] 2.186706 2.186706 2.201231 2.229989 2.272442 2.327842 2.395289
[57] 2.473805 2.562400 2.660098 2.765980 2.879219 2.999078 3.124907
[64] 3.256161 3.392390 3.533217 3.678339 3.827533 3.980627 4.137493
[71] 4.298051 4.462261 4.630100 4.801568 4.976689 5.155487 5.337992
[78] 5.524238 5.714254 5.908057 6.105658 6.307056 6.512232 6.721152
[85] 6.933766 7.150007 7.369790 7.593014 7.819562 8.049302 8.282091
[92] 8.517775 8.756191 8.997169 9.240537 9.486125 9.733759 9.983272
[99] 10.234514 10.487335
[[28]][[1]]$raw
[1] 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
[16] 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
[[28]][[1]]$xlab
[1] "YEAR"
[[28]][[1]]$ylab
[1] "s(YEAR,1.11)"
[[28]][[1]]$main
NULL
[[28]][[1]]$se.mult
[1] 2
[[28]][[1]]$xlim
[1] 1978 2007
[[28]][[1]]$fit
[,1]
[1,] -8.62312353
[2,] -8.43277139
[3,] -8.24242900
[4,] -8.05210610
[5,] -7.86181268
[6,] -7.67156252
[7,] -7.48137242
[8,] -7.29125927
[9,] -7.10124129
[10,] -6.91133988
[11,] -6.72157695
[12,] -6.53197461
[13,] -6.34255702
[14,] -6.15334933
[15,] -5.96437672
[16,] -5.77566511
[17,] -5.58724146
[18,] -5.39913286
[19,] -5.21136649
[20,] -5.02397005
[21,] -4.83697143
[22,] -4.65039850
[23,] -4.46427910
[24,] -4.27864103
[25,] -4.09351209
[26,] -3.90891990
[27,] -3.72489156
[28,] -3.54145405
[29,] -3.35863430
[30,] -3.17645841
[31,] -2.99495194
[32,] -2.81414048
[33,] -2.63404894
[34,] -2.45470106
[35,] -2.27612044
[36,] -2.09833043
[37,] -1.92135278
[38,] -1.74520862
[39,] -1.56991904
[40,] -1.39550381
[41,] -1.22198118
[42,] -1.04936933
[43,] -0.87768579
[44,] -0.70694582
[45,] -0.53716413
[46,] -0.36835532
[47,] -0.20053180
[48,] -0.03370444
[49,] 0.13211593
[50,] 0.29691975
[51,] 0.46070016
[52,] 0.62345068
[53,] 0.78516522
[54,] 0.94584066
[55,] 1.10547526
[56,] 1.26406731
[57,] 1.42161714
[58,] 1.57812788
[59,] 1.73360285
[60,] 1.88804616
[61,] 2.04146545
[62,] 2.19386936
[63,] 2.34526664
[64,] 2.49566882
[65,] 2.64508983
[66,] 2.79354369
[67,] 2.94104569
[68,] 3.08761461
[69,] 3.23326977
[70,] 3.37803080
[71,] 3.52192036
[72,] 3.66496279
[73,] 3.80718244
[74,] 3.94860527
[75,] 4.08925985
[76,] 4.22917500
[77,] 4.36837996
[78,] 4.50690636
[79,] 4.64478665
[80,] 4.78205330
[81,] 4.91873994
[82,] 5.05488139
[83,] 5.19051251
[84,] 5.32566836
[85,] 5.46038456
[86,] 5.59469683
[87,] 5.72864086
[88,] 5.86225169
[89,] 5.99556391
[90,] 6.12861212
[91,] 6.26142977
[92,] 6.39404814
[93,] 6.52649819
[94,] 6.65881029
[95,] 6.79101060
[96,] 6.92312351
[97,] 7.05517331
[98,] 7.18717996
[99,] 7.31915808
[100,] 7.45112194
[[28]][[1]]$plot.me
[1] TRUE
for(i in 1:length(gamls)){
plot(gamls[[i]], main = dls[[i]]$valid_name[1])
}# species to keep:
ex = ex[c(1,4,12,13,16,18,21,23,26,28)]
d_crop = dplyr::filter(d_crop, valid_name %in% ex)4.3.2 Build an mvgam model for all species together
4.3.2.1 Prepare the data
# format into long
dat = d_crop |>
select(valid_name, ABUNDANCE, YEAR) |>
rename("time" = "YEAR",
"series" = "valid_name",
"y" = "ABUNDANCE")
dat$y = as.vector(dat$y)
dat <- filter(dat, series != "Vireo olivaceus")
dat$series <- as.factor(dat$series)
dat$time <- as.integer(dat$time)-min(dat$time)
data_train = dat[which(d_crop$YEAR <= 1999),]
data_test = dat[which(d_crop$YEAR > 2000),]
ggplot(data = data_train) +
geom_smooth(aes(x = time, y = y,
col = series, fill = series),
alpha = .1) +
colorspace::scale_color_discrete_qualitative() +
colorspace::scale_fill_discrete_qualitative() `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
4.3.2.2 Prepare the priors
npops <- length(unique(data_train$series))
knots <- 4
mvgam_prior <- mvgam(
data = data_train,
formula = y ~
s(time, bs = "tp", k = knots) +
s(series, bs = "re", k = npops),
family = "poisson",
trend_model = "GP",
chains = 3,
use_stan = TRUE,
prior_simulation = TRUE
)
test_priors <- get_mvgam_priors(
y ~ s(time, bs = "tp", k = knots) +
s(series, bs = "re", k = npops),
family = "poisson",
data = data_train,
trend_model = "GP",
use_stan = TRUE
)
plot(mvgam_prior, type = "smooths")4.3.2.2.1 Check the number of knots
knots = 4
npops <- length(unique(data_train$series))
hgam = mgcv::gam(y ~ s(time, bs = "tp", k = 5) +
s(series, bs = 're', k = npops),
family = "poisson",
data = data_train)
mgcv::gam.check(hgam)
Method: UBRE Optimizer: outer newton
full convergence after 10 iterations.
Gradient range [6.015154e-16,1.222171e-06]
(score 2.076686 & scale 1).
Hessian positive definite, eigenvalue range [0.0003777539,0.003389441].
Model rank = 15 / 15
Basis dimension (k) checking results. Low p-value (k-index<1) may
indicate that k is too low, especially if edf is close to k'.
k' edf k-index p-value
s(time) 4.00 1.81 0.93 0.16
s(series) 10.00 8.96 NA NA
plot(hgam)4.3.2.3 Train the model on data
#m1 <- mvgam(data = data_train,
# formula = y ~ s(time, bs = "tp", k = 5) +
# s(series, bs = "re"),
# use_lv = FALSE,
# family = "poisson",
# trend_model = 'GP',
# use_stan = TRUE,
# chains = 2,
# burnin = 5000,
# samples = 10000)
#saveRDS(m1, paste0("variance/outputs/mvgam_variance.rds"))
m1 <- readRDS(here::here("variance", "outputs", "mvgam_variance.rds"))4.3.3 Plots and model outputs
4.3.3.1 Visualize model diagnostics and smooths
plot(m1) # Basic model diagnostic plotsmvgam::plot_mvgam_smooth(m1) # Plot estimated smooth functionsmvgam::plot_mvgam_randomeffects(m1) # Plot random effectsdat$series |> unique() # List all unique series included in the dataset [1] Agelaius phoeniceus Spinus tristis Catharus guttatus
[4] Setophaga coronata Setophaga virens Melospiza melodia
[7] Mniotilta varia Seiurus aurocapilla Turdus migratorius
[10] Vireo solitarius
10 Levels: Agelaius phoeniceus Catharus guttatus ... Vireo solitarius
4.3.3.2 Species associations
library(here)
#sp_corr = mvgam::lv_correlations(m1) # Extract latent variable (species) correlation matrix
sp_corr <- readRDS(here::here("variance", "outputs", "sp_corr_variance.rds"))
# name cleanup
colnames(sp_corr$mean_correlations) <- gsub("_", " ", colnames(sp_corr$mean_correlations)) |>
stringr::str_to_sentence()
rownames(sp_corr$mean_correlations) <- gsub("_", " ", rownames(sp_corr$mean_correlations)) |>
stringr::str_to_sentence()4.3.3.3 Plot as a heatmap
Visualize and summarize species (latent variable) correlations from the model
corrplot::corrplot(sp_corr$mean_correlations,
type = "lower",
method = "color",
tl.cex = 2.5, cl.cex = 3, tl.col = "black", font = 13)Warning in corrplot::corrplot(sp_corr$mean_correlations, type = "lower", : Not
been able to calculate text margin, please try again with a clean new empty
window using {plot.new(); dev.off()} or reduce tl.cex
sp_corr$mean_correlations |> mean()[1] 0.3046276
sp_corr$mean_correlations |> sd()[1] 0.3740284
sp_corr$mean_correlations |> apply(2, mean) Agelaius phoeniceus Bombycilla cedrorum Catharus fuscescens
0.18519932 0.16093650 0.19828996
Catharus guttatus Corvus brachyrhynchos Cyanocitta cristata
0.14082619 0.45574604 0.29879417
Empidonax alnorum Empidonax minimus Geothlypis trichas
0.13669726 0.39534503 0.05228182
Haemorhous purpureus Melospiza georgiana Melospiza melodia
0.36583565 0.32710828 0.41040169
Mniotilta varia Pheucticus ludovicianus Poecile atricapillus
0.31394922 0.10957683 0.31970726
Seiurus aurocapilla Setophaga caerulescens Setophaga coronata
0.11749735 0.07930013 0.42762314
Setophaga pensylvanica Setophaga ruticilla Setophaga virens
0.39327619 0.26250445 0.32853495
Sphyrapicus varius Spinus tristis Spizella passerina
0.42225813 0.34020221 0.49806301
Troglodytes troglodytes Turdus migratorius Vireo solitarius
0.26579594 0.50849813 0.48569396
Zonotrichia albicollis
0.52962935
sp_corr$mean_correlations |> apply(2, sd) |> lines()sp_corr$mean_correlations |> hist()4.4 Step 4: Box 3 - Prediction
4.4.1 Process the data
Here we use d_crop, previously processed in Box 2, and further prepare it for this section.
# Add a rare/undersampled species for Example 1
d_crop_rare <- readRDS(here::here("prediction", "example_rare_species.rds"))
d_crop_merged <- rbind(d_crop, d_crop_rare)
# Rename columns and adjust abundance
dat <- d_crop_merged %>%
rename(
y = ABUNDANCE,
series = valid_name, # for the mvgam requirement
lat = LATITUDE,
long = LONGITUDE,
time = YEAR # for the mvgam requirement
)
dat <- dat %>%
group_by(time) %>%
mutate(total_abun = sum(y)) %>%
mutate(rel_abun = y / total_abun) %>%
select(-total_abun)4.4.1.1 mvgam format requirements
Prepare and format the dataset for HGAM fitting and forecasting: adjust columns to meet mvgam requirements, define training/testing subsets, and create datasets with and without specific species for out-of-sample forecasts.
## Adjust columns for mvgam requirements
dat$y <- as.vector(dat$y)
dat <- filter(dat, series != "Vireo olivaceus")
dat$series <- as.factor(dat$series)
dat$time <- as.integer(dat$time) - min(dat$time)
# Subset the data in training and testing folds
data_train <- dat[which(d_crop$YEAR <= 1999), ]
data_test <- dat[which(d_crop$YEAR > 2000), ]
# subsetting the data with and without a species for out-of-sample forecasting
# Remove Setophaga pinus due to missing observations in some years
data_noMniotilta <- filter(dat, series != "Mniotilta varia" & series != "Setophaga pinus")
data_Mniotilta <- filter(dat, series == "Mniotilta varia")4.4.2 Fit Models
4.4.2.1 Inspect and visualize training and testing data
Finalize and visualize data subsets: unused factor levels are removed, the temporal extent of the test set is verified, and all series are plotted to assess coverage between training and testing periods.
set.seed(2505)
data_train <- data_train %>%
droplevels()
data_test <- data_test %>%
droplevels()
range(data_test$time)[1] 23 29
# Plot series
plot_mvgam_series(
data = data_train,
newdata = data_test,
series = "all"
)4.4.2.2 Penalized splines forecast: mod_forecast_ps
A State-Space hierarchical GAM is fitted using a Poisson family, AR(1) temporal dynamics, and penalized spline smooths. The model structure incorporates hierarchical time effects for computational efficiency and summarizes key outputs excluding beta estimates.
# Set up a State-Space hierarchical GAM with AR1 dynamics for autocorrelation
# Smooths are penalized splines
# mod_forecast_ps <- mvgam(
# data = data_train,
# formula = y ~
# s(series, bs = "re"),
#
# # Hierarchical smooths of time set up as a
# # State-Space model for sampling efficiency
# trend_formula = ~
# s(time, bs = "tp", k = 6) +
# s(time, trend, bs = "sz", k = 6),
# family = poisson(),
#
# # AR1 for "residual" autocorrelation
# trend_model = AR(p = 1),
# noncentred = TRUE,
# priors = prior(exponential(2),
# class = sigma
# ),
# backend = "cmdstanr"
# )
# Read the model
mod_forecast_ps <- readRDS(here::here("prediction", "output", "mod_nick.rds"))4.4.2.2.1 Model summary
summary(mod_forecast_ps, include_betas = FALSE)GAM observation formula:
y ~ +s(series, bs = "re")
GAM process formula:
~s(time, bs = "tp", k = 6) + s(time, trend, bs = "sz", k = 6)
Family:
poisson
Link function:
log
Trend model:
AR(p = 1)
N process models:
10
N series:
10
N timepoints:
22
Status:
Fitted using Stan
4 chains, each with iter = 1000; warmup = 500; thin = 1
Total post-warmup draws = 2000
GAM observation model coefficient (beta) estimates:
2.5% 50% 97.5% Rhat n_eff
(Intercept) -1.1 2.7 6.1 1 1516
GAM observation model group-level estimates:
2.5% 50% 97.5% Rhat n_eff
mean(s(series)) -1.90 -0.025 1.9 1 3102
sd(s(series)) 0.45 0.750 1.4 1 757
Approximate significance of GAM observation smooths:
edf Ref.df Chi.sq p-value
s(series) 8.88 10 85.8 0.1
Process model AR parameter estimates:
2.5% 50% 97.5% Rhat n_eff
ar1[1] -0.072 0.52000 0.94 1.01 522
ar1[2] -0.590 -0.00310 0.68 1.00 521
ar1[3] -0.710 0.35000 0.94 1.00 869
ar1[4] -0.370 0.33000 0.89 1.00 840
ar1[5] -0.820 0.00970 0.88 1.00 948
ar1[6] -0.350 0.25000 0.87 1.00 500
ar1[7] -0.860 0.06900 0.91 1.00 1301
ar1[8] -0.900 -0.02100 0.91 1.01 1295
ar1[9] -0.480 0.21000 0.85 1.01 749
ar1[10] -0.780 0.00031 0.89 1.00 1609
Process error parameter estimates:
2.5% 50% 97.5% Rhat n_eff
sigma[1] 0.3100 0.47 0.71 1.00 876
sigma[2] 0.2500 0.41 0.65 1.00 705
sigma[3] 0.0097 0.21 0.46 1.00 376
sigma[4] 0.1600 0.41 0.73 1.00 766
sigma[5] 0.0076 0.14 0.31 1.00 497
sigma[6] 0.2500 0.43 0.68 1.00 748
sigma[7] 0.0033 0.10 0.30 1.00 624
sigma[8] 0.0058 0.17 0.53 1.01 665
sigma[9] 0.0740 0.17 0.30 1.00 843
sigma[10] 0.0047 0.10 0.30 1.00 821
GAM process model coefficient (beta) estimates:
2.5% 50% 97.5% Rhat n_eff
(Intercept)_trend -3.5 0.057 3.7 1 1530
Approximate significance of GAM process smooths:
edf Ref.df Chi.sq p-value
s(time) 0.584 5 9.56 0.0038 **
s(time,series) 1.256 54 10.22 1.0000
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Stan MCMC diagnostics:
n_eff / iter looks reasonable for all parameters
Rhat looks reasonable for all parameters
0 of 2000 iterations ended with a divergence (0%)
1106 of 2000 iterations saturated the maximum tree depth of 10 (55.3%)
*Run with max_treedepth set to a larger value to avoid saturation
E-FMI indicated no pathological behavior
Samples were drawn using NUTS(diag_e) at Wed Oct 15 1:39:31 PM 2025.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split MCMC chains
(at convergence, Rhat = 1)
4.4.2.2.2 Plots
# Plot random effects
mvgam::plot_mvgam_randomeffects(mod_forecast_ps)# Condtional effects
conditional_effects(mod_forecast_ps)# Forecast penalized splines
forecast_penalized_splines <- plot_predictions(
mod_forecast_ps,
by = c("time", "series", "series"),
newdata = datagrid(
time = 1:max(data_test$time),
series = unique
),
type = "expected"
)
forecast_penalized_splinesObviously the splines show high extrapolation uncertainty into the test time points, but that is ok as it isn’t the focus of this exercise. But if we wanted better forecasts, let’s use GPs in place of the penalized smooths. Source used.
4.4.2.2.3 Look at some of the AR1 estimates
# Look at some of the AR1 estimates
mcmc_plot(mod_forecast_ps, variable = "ar1", regex = TRUE)4.4.2.3 Gaussian process forecasts : mod_forecast_GP
This model replaces penalized spline smooths with Gaussian Process terms to more flexibly model temporal dependencies and enhance forecasting accuracy.
# Using Gaussian Process in place of penalized smooths to get better forecasts
# mod_forecast_GP <- mvgam(
# data = data_train,
# formula = y ~
# s(series, bs = "re"),
#
# # Hierarchical smooths of time set up as a
# # State-Space model for sampling efficiency
# trend_formula = ~
# gp(time, k = 6) +
# s(time, trend, bs = "sz", k = 6),
# family = poisson(),
#
# # AR1 for "residual" autocorrelation
# trend_model = AR(p = 1),
# noncentred = TRUE,
# priors = prior(exponential(2),
# class = sigma
# ),
# backend = "cmdstanr"
# )
# Read the model
mod_forecast_GP <- readRDS(here::here("prediction", "output", "mod_nick_GP.rds"))4.4.2.3.1 Model summary
summary(mod_forecast_GP, include_betas = FALSE)4.4.2.3.2 Predict
# # Build prediction grid
# pred_data <- data.frame(
# time = rep(1:max(data_test$time), each = length(unique(data_train$series))),
# series = rep(unique(data_train$series), times = max(data_test$time))
# )
#
# predictions <- predictions(
# mod_forecast_GP,
# newdata = pred_data,
# by = c("time", "series", "series"),
# type = "expected"
# )
#
# # Mark which points are forecasts & Add a vertical line where the train test splits (time = 22)
# predictions$forecast <- ifelse(predictions$time > 22, "Forecast", "Fitted")4.4.2.3.3 Plot species-level forecasts
# ggplot(predictions, aes(x = time, y = estimate)) +
# geom_ribbon(
# aes(ymin = conf.low, ymax = conf.high, fill = series),
# alpha = 0.2
# ) +
# geom_line(
# data = subset(predictions, forecast == "Fitted"),
# aes(color = series), linewidth = 1
# ) +
# geom_line(
# data = subset(predictions, forecast == "Forecast"),
# aes(color = series), linewidth = 1, linetype = "dashed"
# ) +
# geom_vline(xintercept = 22, linetype = "dotted") +
# geom_point(data = data_train, aes(x = time, y = y), alpha = 0.2) +
# geom_point(data = data_test, aes(x = time, y = y), alpha = 0.2) +
# facet_wrap(~series, scales = "free_y") +
# theme(
# legend.position = "none",
# strip.text = element_text(size = 14, face = "italic")
# ) +
# labs(y = "Abundance", x = "Time") +
# theme(axis.title = element_text(size = 14))4.4.2.3.4 Plot latent/global trend
# plot_predictions(
# mod_nick_GP,
# by = c("time"),
# newdata = datagrid(
# time = 1:max(data_test$time),
# series = unique
# ),
# type = "expected"
# ) +
# geom_vline(xintercept = 22, linetype = "dotted") +
# labs(y = "Global latent trend", x = "Time") +
# theme(axis.title = element_text(size = 14))4.4.3 Gaussian process - predicting new species
4.4.3.1 Black-and-white Warbler (BAWW) Post-stratification model
4.4.3.1.1 Training dataset & train the model
In this section, we prepare a training dataset that excludes Mniotilta varia (Black-and-white Warbler) to perform post-stratification. We examine missing observations across species and time, verify data completeness, and then load the fitted state-space HGAM (Gaussian Process–based) trained on the reduced dataset.
# # Black-and-white Warbler Post-stratification Model ----
# # Create training data excluding Mniotilta varia (Black-and-white Warbler)
# data_train_noBAWW <- data_noMniotilta %>%
# droplevels()
#
# # Set up State-Space hierarchical GAM excluding BAWW for post-stratification
# set.seed(2505)
# data_train_noBAWW %>%
# group_by(series) %>%
# summarise(
# n_obs = n(),
# expected_obs = length(unique(data_train_noBAWW$time)),
# missing_obs = expected_obs - n_obs
# ) %>%
# filter(missing_obs > 0)
# unique(data_train_noBAWW$series)
#
#
# colSums(is.na(data_train_noBAWW))
# mod_strat_BAWW <- mvgam(
# data = data_train_noBAWW,
# formula = y ~
# s(series, bs = "re"),
#
# # Hierarchical smooths of time set up as a
# # State-Space model for sampling efficiency
# trend_formula = ~
# gp(time, k = 3, gr = FALSE),
# family = poisson(),
#
# # AR1 for "residual" autocorrelation
# trend_model = AR(p = 1),
# noncentred = TRUE,
# priors = prior(exponential(2),
# class = sigma
# ),
# backend = "cmdstanr"
# )
# Read the model
# mod_strat_BAWW <- readRDS(here::here("prediction", "output", "mod_strat_BAWW.rds"))4.4.3.1.2 Construct weighted prediction data for post-stratification
# # Post-stratification for Black-and-white Warbler prediction ---
# # predict trends for all species and weight these based
# # on their "distance" to the new species
# unique_species_noBAWW <- levels(data_train_noBAWW$series)
#
# # Add some weights; here a higher value means that species is "closer" to the
# # un-modelled target species. This could for example be the inverse of a phylogenetic
# # or functional distance metric
#
# # Initialize all weights to 1
# species_weights_BAWW <- rep(1, length(unique_species_noBAWW))
# names(species_weights_BAWW) <- unique_species_noBAWW
#
# # Assign higher weight to warblers species
# # Weight it 10x higher than other species for strong post-stratification
#
# setophaga_species <- grep("Setophaga", unique_species_noBAWW, value = TRUE)
# species_weights_BAWW[setophaga_species] <- 10
# species_weights_BAWW["Seiurus aurocapilla"] <- 10
#
#
# # Generate the prediction grid; here we replicate each species' temporal grid
# # a number of times, with the number of replications determined by the weight
# # vector above
# pred_dat_BAWW <- do.call(
# rbind,
# lapply(seq_along(unique_species_noBAWW), function(sp) {
# sp_name <- unique_species_noBAWW[sp]
# weight <- species_weights_BAWW[sp_name]
#
# do.call(
# rbind,
# replicate(
# weight,
# data.frame(
# time =
# 1:max(data_train_noBAWW$time + 1), # time is indexed starting at 0
# series = sp_name
# ),
# simplify = FALSE
# )
# )
# })
# ) %>%
# dplyr::mutate(
# series = factor(series, levels = levels(data_train_noBAWW$series))
# )4.4.3.1.3 Get post-stratified predictions
# Generate post-stratified predictions for Black-and-white Warbler
# Marginalize over "time" to compute weighted average predictions
# post_strat_BAWW <- marginaleffects::avg_predictions(
# mod_strat_BAWW,
# newdata = pred_dat_BAWW,
# by = "time",
# type = "expected"
# )4.4.3.1.4 Visualize post-stratified predictions for BAWW
We compare the post-stratified predictions for Mniotilta varia (Black-and-white Warbler) with the observed abundance data from the original dataset. The plot displays the predicted trend with 95% credible intervals (shaded area) alongside the empirical observations, allowing for a visual assessment of how well the post-stratified model captures the species’ temporal dynamics.
# Visualization: Post-stratified BAWW predictions ----
# Plot the post-stratified trend predictions for Black-and-white Warbler
# Compare with actual BAWW data from the original dataset
# actual_BAWW_data <- dat %>%
# filter(series == "Mniotilta varia")
# plot_BAWW_poststrat <- ggplot(post_strat_BAWW, aes(x = time, y = estimate)) +
# geom_ribbon(aes(ymax = conf.high, ymin = conf.low),
# colour = NA, fill = "steelblue", alpha = 0.4
# ) +
# geom_line(colour = "steelblue", linewidth = 1.2) +
# geom_point(
# data = actual_BAWW_data,
# aes(x = time, y = y),
# colour = "black", alpha = 0.7, size = 2
# ) +
# theme_classic() +
# labs(
# y = "Abundance (Black-and-white Warbler)",
# x = "Time"
# ) +
# theme(
# plot.title = element_text(size = 12),
# plot.subtitle = element_text(size = 10)
# )
#
# print(plot_BAWW_poststrat)4.4.3.1.5 Anchor and evaluate Post-stratified predictions for BAWW model
To align the post-stratified forecasts with observed data, we anchor the predictions by calibrating the intercept using the first year of Mniotilta varia (Black-and-white Warbler) observations. The offset ensures that predicted abundances match the empirical baseline. We then assess model performance using MAE and RMSE, and compare prediction agreement with a standard GAM by examining correlation and directional trend consistency between the two models.
# # Anchored Post-stratified BAWW Model ----
# # Use first year of BAWW data to calibrate the intercept of post-stratified predictions
#
# # Get the first year BAWW observation for anchoring
# first_year_BAWW <- actual_BAWW_data %>%
# filter(time == 0)
#
# # Find the post-stratified prediction for the same time point
# first_year_pred <- post_strat_BAWW %>%
# filter(time == 1)
#
# # Calculate the offset needed to match observed abundance
# abundance_offset <- first_year_BAWW$y - first_year_pred$estimate
#
# # Apply offset to all post-stratified predictions
# post_strat_BAWW_anchored <- post_strat_BAWW %>%
# mutate(
# estimate_original = estimate,
# conf.low_original = conf.low,
# conf.high_original = conf.high,
# estimate = estimate + abundance_offset,
# conf.low = conf.low + abundance_offset,
# conf.high = conf.high + abundance_offset
# )
#
# mvgam_pred_mean <- post_strat_BAWW_anchored$estimate
# mae_mvgam <- mean(abs(data_Mniotilta$y - mvgam_pred_mean))
# rmse_mvgam <- sqrt(mean((data_Mniotilta$y - mvgam_pred_mean)^2))
#
#
# # GAM for BAWW
# BAWW_gam <- gam(y ~ s(time), data = data_Mniotilta)
#
#
# # Calculate correlation between predictions
# cor_predictions <- cor(mvgam_pred_mean, gam_pred)
# cor_predictions
#
# # Direction of trend agreement
# gam_trend_direction <- sign(diff(gam_pred))
# mvgam_trend_direction <- sign(diff(mvgam_pred_mean))
# trend_agreement <- mean(gam_trend_direction == mvgam_trend_direction)
# trend_agreement4.4.3.1.6 Visualize anchored versus original post-stratified predictions
This plot compares the anchored post-stratified predictions for Mniotilta varia (Black-and-white Warbler) with the observed abundance data. The anchored model, shown with a dashed green line and shaded credible interval, represents predictions adjusted to match the observed baseline, allowing visual assessment of the calibration effect relative to the original post-stratified estimates.
# Visualization: Anchored vs Original Post-stratified Predictions ----
# plot_BAWW_anchored <- ggplot() +
# # Anchored post-stratified prediction
# geom_ribbon(
# data = post_strat_BAWW_anchored,
# aes(x = time, ymin = conf.low, ymax = conf.high),
# fill = "darkgreen", alpha = 0.4
# ) +
# geom_line(
# data = post_strat_BAWW_anchored,
# aes(x = time, y = estimate),
# color = "darkgreen", size = 1.2, linetype = "dashed"
# ) +
#
# # Actual BAWW data
# geom_point(
# data = actual_BAWW_data,
# aes(x = time, y = y),
# colour = "black", alpha = 0.2, size = 2.5
# ) +
# theme_classic() +
# labs(
# y =
# expression(paste("Predicted ", italic("Mniotilta varia"), " abundance")),
# x = "Time"
# ) +
# theme(
# axis.title = element_text(size = 12),
# legend.position = "none"
# )5 References
Clark, N. (2023). Temporal autocorrelation in GAMs and the mvgam package. https://ecogambler.netlify.app/blog/autocorrelated-gams/
Pardieck, K. L., Ziolkowski Jr., D. J., and Hudson, M. A. R. (2015). North American Breeding Bird Survey Dataset 1966 - 2014, version 2014.0. https://biotime.st-andrews.ac.uk/selectStudy.php?study=195
Pedersen, E. J., Miller, D. L., Simpson, G. L., & Ross, N. (2019). Hierarchical generalized additive models in ecology: an introduction with mgcv. PeerJ, 7, e6876.
Pedersen, E. J., Koen-Alonso, M., & Tunney, T. D. (2020). Detecting regime shifts in communities using estimated rates of change. ICES Journal of Marine Science, 77(4), 1546-1555